Spiritualist was planning to do a spin-off (an "AH within an AH") where Reagan beat Humphrey in '76 (only three electoral votes seperated them) but, as the main page shows, he last updated his site in 2002.
We always need more AH authors… but Reagan almost certainly would have gone up against Humphrey (and, in my opinion, probably won) in '72.
As for Humphrey winning in '68 I imagine that given four years he could have consolidated the Great Society somewhat, with an outside chance at passing healthcare… Viet Nam, of course, is the big question.
In likelihood Humphrey does follow withdrawal along Nixon's Vietnamization albeit sooner. Something similar to what RFK would probably have done had he lived/won.
How that works out for South Vietnam… is hard to say. It's entirely possible that South Vietnam could have held out for a very long time with sufficient US dollars and air power, but naturally American commitment may wane as—unlike Korea—they remain involved in combat, not just troops stationed there. Also, public opinion without a POD involving the Tet Offense is against the war and Humphrey may/may not be better at managing it than Nixon did.
Politically Humphrey's victory is short lived and illusory, achieved with the lingering non-Southern elements of FDR's coalition and with Wallace siphoning enough Southern voters so that Nixon didn't win based on the South.
However in '72 Reagan will take the South, California & the Far West, the Midwest, probably Texas, and probably enough blue collar states (Ohio, New Jersey, Michigan, Pennsylvania) to beat Humphrey.
The key thing to note about the Democratic Party is that Humphrey, and other old school liberals, are far more appealing to "Reagan Democrats". Although they pushed civil rights they generally—as with FDR—focused little on other social issues such as gay rights, abortion, and so on. From McGovern onwards the Democratic Party pushed away those voters with a combination of talking about social issues and the Republicans (led by Nixon) clervery using social issues as a wedge.
No McGovern and no Nixon and four years of Humphrey almost certainly leave the Democratic Party better able to compete as their economic position (popular with voters) remains more important than social issues. The South is still gone, but Rust Belt should like the Democrats more than OTL.
This depends, of course, on the next couple Democratic nominees and how well both Democrats and Republicans handle social issues.
One thing to note is that '72 Reagan is not a supply-sider. His administration would a libertarian leaning version of Gerald Ford or Jimmy Carter. Probably military reform, deregulation, and lower taxes paid for with some program cuts (unlike OTL).
So the hypothetical US of 1976 or so is probably heading towards a balanced budget, able to handle the oil shocks much better than in OTL, earlier deregulation & military reform but also a Great Society that saw four years of fine tuning (instead of Nixon ignoring it) which could help certain areas where the Great Society was successful in OTL—poverty, most notably.
Our hypothetical Democratic Party remains fairly old school liberal, mixed with some new school DLC types and with New Left/social issue liberals more on the sidelines. A mix of Teddy Kennedy and Gary Hart, say.
The Republican Party is interesting. Four to eight years of Reagan have probably taken out the need for supply-side voodoo economics (in that the Republicans are seeing electoral success with a libertarian-ish/real conservative in a way they don't consider Eisenhower/Nixon to be IOTL) which is only a plus for the US budget.
Without Nixon the Republicans are less successful in exploiting social issues (especially if Roe Vs. Wade is butterflied) which probably leaves the Gerald Ford moderate-to-conservative wing still powerful (Rockefeller Republicans are still screwed) alongside a Western/libertarian wing. The neo-conservatives are likely still a major power base, but to OTL's extent.
This leaves social conservatives in the South somewhat marginalized, but with the Democrats still being a worse options. However the Democrats will probably remain more competitive than IOTL (although perhaps not at a Presidential level).
(Alternatively things end up much as they are IOTL with Reagan following Nixon's playbook upon winning in '72.)
