By the way, the issue of one of the three Senate classes synchronizing with the fixed Presidential 6 year cycle instead of having that roll through all three evenly might be addressed by a very very simple reform--move the Senate elections to odd numbered years. That way, it remains true that two of three classes flank the Presidential election, and a third is permanently isolated. But the 12 month separation might be enough. Of course this demands elections every damn year, in states where elections normally are in even years--a minority do hold state office elections in odd years though. Now the people who wanted direct election of Senators probably won't be too fazed by increasing the cost burden of government by having to hold elections every year, they'd probably judge that a small price to pay for better democracy, and as far as the utility of monkeying around with detailed mechanisms goes, I'd agree. More frequent elections, other things being equal, are a good thing in themselves--depending on details, they can be bad of course. It probably is not a great idea to elect the House of Representatives to single year terms for instance, that gives very little time to get up to speed on legislative business before the next election cycle is in full swing. (OTOH, we could say apportion half as many districts are there are House members--say a House of 500 members, and 250 districts, and have two "classes" of Representatives overlapping each other for a lite form of Senate style staggering, with each district, about half as many as OTL, or rather more like 55 percent as many with 9/5 as many states with given small numbers of districts, one two or three, electing a single Rep each year. This would tend to shift apportionment of total numbers per state down toward the smaller states of course, but I suspect that has less effect on overall partisan balance than one might guess!)
By the way, an Amendment, or I think even mere Congressional legislation, to do this, could also increase the size of the Senate 50 percent and thus give each state a Senator in all three classes. OTL, certainly in the current era and I would guess generally throughout the Senate's history, the chance pattern of state populations that have a Senator in a given Class have evolved to make the class elections very lopsided in terms of what percentage of the whole nation can vote for a given Senate class. With the current numbers of Senators, 100 in 50 states, one class, IIRC Class 3, has 34 members and the other two are both 33. Close to 2/3 of all states have a Senate election in a given (currently even numbered) election year, but if each group of states had the same overall population summed up we'd expect that to be 2/3 the national population too--in fact, though, Class 2 has evolved to have little over half US population, which means the other two must average nearly 3/4--Class 1 is largest near 80 percent IIRC, and Class 3 though smaller is still well over 2/3. The recent pattern of partisan strength in the states has also made Class 2 lean strongly Republican these days.
So--making every state elect one of three Senators in each class would go a long way toward smoothing out the US political cycle so that shifts in actual national voting patterns are more faithfully reflected in the composition of the Senate.
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Now, I'd like to dig deeper into the philosophical dialog that toyed with the single six year term versus the opposition Wilson (and I presume many others) put forth on various grounds. A dialog resulting in a modified proposal that is admittedly weirder but perhaps better might go like this:
As Wilson observes, four years may already be too long for a mediocre to bad President to hold office. We can hardly contemplate shortening the term down a lot below four years though. Whereas if a President as Wilson so loftily puts it has some "great work" in process, as Wilson suggests with the support of the majority of voters, as he says, even eight might not be enough--but to get Wilson or others advocating no term limits to compromise, they probably would have to agree that if a "great work" is both so plainly needed and so confidently entrusted to one leader, surely that Great Leader has close followers and comrades whom they can entrust the Great Work to. If barred from electing a beloved and effective President with solid popularity, surely that admired President will be listened to when he or she says "behold my anointed son or daughter, my loyal and astute and diligent lieutenant who has stood by our great shared causes and worked to bring them to fruition, heed my recommendation and endorsement, this is the one who will continue our hard work and the one you can trust as I do!" Surely, if the people are flocking to support one leader, they have been paying attention to whom their friends and foes have been and know their trusted President speaks truth and good sense, and therefore no harm is done by the admired one standing aside to retire, with such an able successor at hand! So, in compromise, the Wilsonians agree that some finite term limit is no terrible disaster, for any Great Work worth doing has many supporters, and the term-limit hawks agree that an eight year cap has been tried and true throughout the history of the Constitution, and is not excessively long.
So--each election that elects a new person to the Presidency gives that new President not four but only three years before the next election. However if the incumbent President newly elected in one year should be a major candidate in that election 3 years hence, after they have actually held office from inauguaration (practically in April back then, that is a week and a half or so before the end of March) until November three years after their election, thus 32 plus months of actual power, two and 2/3 years, is elected again, it can be presumed that a majority or anyway the largest plurality of American voters have had a fair chance to judge the President by their deeds as well as words, and decided they are good enough--better than any rival who presented themselves to contest the office anyway. In the general spirit of how our winner take all processes work, we could simply grant any President reelected after three years in power not 3 or 4 but 5 years of office. It adds up to 8, same as when Americans customarily reelect a President for two 4 year terms.
(To elaborate optionally, taking Wilson at his word that the kind of President we want to see retained in office should be kept because a majority of American voters judge them the best--flexible term lengths allow a compromise when the plurality falls short of the majority. Observing that the Constitution as written and then amended in the 12th Amendment takes no notice of popular vote, someone speaking in Wilson's grand language about the mandate of the people should bloody well be asked to agree this Amendment by the way stipulates that each state shall in some fashion conduct and follow a popular vote, making what constitutionally is hitherto a popular custom into a binding requirement. With that possible loophole against PV relevance closed, a President who gets the majority of EV, or is elected by the House, but fails to get a solid majority of popular votes, is reelected, but only for 3 more years, not 5).
Thus, any amended Constitutional bar to a President's reelection would be based on their winning a second, 5 year term.
The term limit hawks could demand this is an absolute lifetime prohibition on their ever being elected again; those claiming to favor leaving the choice up to the people could suggest it is merely a bar against their running in a third election successively, with the clock reset to zero after the next, necessarily 3 year term, has passed. What is feared after all is that one person might create a machine of patronage and possibly even coercive abuse of executive power--a three year cooling off period where some other hand is on the switches legally anyway (surely some strong Boss might try to keep power behind the throne while in nominal retirement) might arguably be plenty of time to defuse and expose such abuses; a respected Leader of Great Works might then reasonably be allowed to stand for another 3 and optionally 8 year round.
A variation on this theme--let the reelected President, after their Washingtonian blessed 8 years, have a choice--to put themselves forth for just two more years more and then, having chosen that option, being barred from ever being elected again, versus stepping down and being eligible to run through another electoral gamut three years later. This gives the Great Leaders the option of an extension to get the Great Works finished already, versus the hope that after a suitable time out, they will again be elected to pick up where they left off for more extensive ongoing projects.
Supposing that in this dialectic, the options for further extensions are rejected, and the 8 year limit affirmed, but on these semi-Wilsonian terms--every new President comes under review earlier, three years after their first election, and if they win reelection, the next election is pushed back two years to give someone who passed electoral mandate twice extra time to manifest their long view voters three years apart approved.
OTOH, no linkage of second term length of 5 years to popular vote majority either, and no messing around with mandates on states as to how to cast their EV. A linkage of a term shorter than 5 years, 3 years or even say just a portion of one (as in interim caretaker until a do-over general election can be held the next November) could be specified in the case a President is chosen by the House and fails to win a majority of EV--but that has not actually happened since 1824! For good reasons, relating to the development of state by state winner take all based on popular vote. So such an elaboration throwing another monkey wrench in the Presidential election calendar is practically speaking a dead letter.
This gives an opportunity too to anticipate another vexed question not settled OTL until the middle of the 20th century--when a President dies or otherwise leaves office before their term has ended, and their VP assumes office, what further provision is there for succession if something then happens to the VP, after or possibly even before they could succeed to office? As with the Booth plot to kill Lincoln; they planned to kill VP Andrew Johnson and the Secretary of State and Treasury too. Emergency succession is something provided for quite early on, in case of such sudden and massive killing off the highest rungs, but no provision was made for a VP who succeeds to office to appoint a new VP for themselves preventing the need to go down that ladder should something later happen to the interim new President in turn.
So--turning to the basic philosophy of this Amendment, that the Presidential authority derives from popular mandate, it should be a principle that no "accidental President" shall serve longer than absolutely necessary. Let's say that it is agreed by the general compromises made that while some cushion of time is needed before a sudden unexpected Presidential election, and such elections should always be held on the customary date stipulated in the Constitution, that is first Tuesday of November, the time between April 1 and that Tuesday, that is seven months plus change in November, is enough--should any President die or otherwise lose office before the end of March in a given year of their term, a new election will be held the November of that very year, any later in the year pushes the election back to the November of the next year.
The VP will serve as President, not subject to any reviews (other than being as liable to impeachment as they were before this crisis) in the interim--and having the power to personally nominate a replacement VP, subject to Senate approval (or some more elaborate process, but not to bog down in that now). This accidental interim service does not count toward any limits.
Glancing over my speculative single term table of winners I guessed at, here is how it might shake out:
Assuming Wilson has none of his prior years of service held against him in 1916, and that election is treated as a brand new bunch of contenders, I do think Wilson will win the same as he did OTL. This qualifies him for not 4 but 3 more years, the next election being in 1919. Now I'd have to delve into details to see if he was in as much trouble by autumn 1919 as he was in 1920 OTL. I am faced with a tossup conundrum right out the gate--but I think I will err on the side of Wilson's chickens coming home to roost that early. After all he wasn't a majority winner in 1912. So the 3-5 Compromise approach shortens his term, he is out by March 1920. I will proceed down the list from there, showing my best guess without commentary as to why!
1916 Wilson
1919 Harding reelected 1922, dies August 1923 as OTL, Coolidge succeeds as interim President
1924 Coolidge, reelected 1927
1932 FDR, reelected 1935
1940 Wallace, reelected 1943
1948 Dewey, declines to run 1951
1951 Eisenhower, reelected 1954
1959 JFK, reelected 1962, assassinated November 1963, LBJ succeeds
1964 LBJ, reelected 1967
1972 Nixon, reelected 1975, resigns 1977, very controversially the day after the deadline to push the election into 1978--succeeded by Ford (or X, maybe GHW Bush, as Ford might have retired from politics by the mid-70s)
1978 Carter, loses reelection bid 1981
1981 Reagan, reelected 1984
1989 GHW Bush, loses reelection bid 1992
1992 Clinton, wins reelection 1995
2000 GW Bush, wins reelection 2003
2008 Obama, wins reelection 2011
2016 Trump, speculation on outcome of election in 2019 withheld as Current Politics.
That's 51 years under Democrats, 49 under Republicans, again much as OTL. Perhaps the Wallace and Johnson administrations not having to faff around with Amendments to mess with details of Presidential succession, they have more political capital to do something else, Puerto Rico statehood or the like, or perhaps reform the Presidential election process to eliminate the Electoral Vote system or modify it to be definitively tied to national PV outcomes (and mandate that popular vote shall indeed be held in the process). Otherwise, again it is remarkable how little such a major reform need change the general shape of the outcomes. And how close the dates coincide despite several monkey wrenches of deaths and resignations being thrown into the works that in this scheme, reset the electoral calendar--but it still settles pretty close to OTL dates anyway, not by any forcing on my part!