Don't forget Seward or Chase. Arfield's youth isn't as much a problem for either as they aren't as ill in 1868. Plus, Seward had those injuries that might have cut his life short by a few years..
On the other hand, I remember reading that Garfield's grandmother was alive when he was inaugurated. While men and women have different genetics so it's not guaranteed he would live a long time, he could easily have become president later than OTL.
It just depends how long you want the Republicans to stay in power. You have a variety of options including just stretching that power through to 1889.
Both Seward and Chase disappointed me in the aftermath of the war. As strange as this may sound, they were too much political for my taste. With this I meant that they always put their own political ambitions ahead of their principles, and while it might be naive to expect a politician to act otherwise, this meant that these ertswhile radicals became almost, or outright Democrats after the war. Seward because he wanted to retain his power in the Johnson administration, even supporting his vetoes of the Freedmen's Bureau and Civil Rights bills; Chase, because he wanted to be President very badly, even dropping his support for Black suffrage in the hopes that the Democrats would pick him. Though they may remain more loyal to Republican principles with Lincoln in charge, it's likely that the prospect of a "conservative coalition" would appeal more to them than to other Republicans.
Assuming Grant does well as President and serves two terms, from 73-1881 that gives us 20 years of uninterrupted Republican rule. It also gives whatever party is going to replace the Dems a good bit of time to work their own kinks out, come to grips with the post-war order and hopefully be able to be a legitimate opposition party that can regain the Presidency at that time and can govern well (because, by 1880, or 1884 at the latest, we're probably going to the GOP lose an election. And the opposition needs to be cleared of those who are goign to try to walk back Civil rights)
I'm not sure if Grant would want to become a governor. In any case, it seems like more executive experience would be a better teacher.
Hopefully we can avoid the railroad corruption the impoversihed the west till the 1960's
Railroads are other issue that I'm working on. The construction of rail lines through the Southern upcountry paradoxically weakened Reconstruction because the isolated White yeomen often resented how opening their communities to external trade changed their lives. It also bankrupted the Reconstruction states.
If Garfield is the head of the anti-Republican Party, then this alt-US may have hit the jackpot in terms of potential party systems. It's a shame Garfield served so little time in the presidency, he really strikes me as one of the people with the most potential in the position.
It's not that unlikely, too, since Garfield was almost lured by the Liberal Republicans but ultimately stayed away. If the split produces a party that earnestly advocated reform without selling their soul to the reactionaries, Garfield may join their ranks.
And to be clear I'm not sure how long it will take for voting rights to be reinstated and for who; save that there will be land redistribution and the planter class is going to bear the brunt of the reconstruction and be more or less destroyed as a class (little loss there). A lot of that was simply musings based on different scenerios I could see. We will need some clarification on that point from @Red_Galiray.
The exact details are being ironed out, but most Confederate civil servants, officials and officers are probably going to be permanently disenfranchised; some common soldiers probably will be disenfranchised for a few years, at least until the new governments get running. The planters, as a class, will be destroyed by a combination of pro-worker economic policies, land redistribution, and the disenfranchisement or outright trial and imprisonment. Even those who managed to retain land or acquire it will see new power dynamics that will make them very different from the old planters, mainly the fact that their workers will have the law and government on their side.
Regarding the very interesting discussion about future party dynamics, my idea was that Republicans will eventually split between the "Labor Republicans" and the "Conservative/National Republicans". The first, for whom I actually prefer the name "Workingmen", would be a big tent party, from true socialists to agrarian populists to merely those discontent with party politics, but their main battle cry would be for reform, state intervention in the economy, and workers' rights. They would attract immigrants in the East and West coast; farmers in the Midwest; and poor Whites and Blacks in the South.
The other Republican faction would become a party that advocates in favor of party machines and big business, and is deadly scared of "communism", wishing instead to maintain "respectable and responsible" economic policy and political dynamics. It would attract industrialists, merchants, middle-class people, in general, those who own the means of production and a comfortable life and thus are content with the status quo.
What's important, however, is that I want both parties to have Black constituencies. Without Jim Crow and with the bigger opportunities of Reconstruction, I envision a Black middle class and bourgeoise ascending. Historically, a small percentage of Black people did achieve middle class status, and they exposed Liberal talking points: the rest of the Black population was merely lazy and improvident, and they could have ascended too if they just tried. I think by the 1880's, those Black people who benefited the most from land redistribution and Reconstruction could come to believe that they obtained it all through hard work and dedication, and that the government ought to not do more because if even after all that help there are still poor Black people it surely must be because they are lazy and worthless, right? Men like Booker T. Washington and Black politicians like Blanche K. Bruce would likely be part of this group, and align themselves with the conservative Republicans. They would be a minority, but 25 to 35 percent of the Black electorate would still make it an attractive plum, especially when such deflections may allow the party in power to carry the South.
Finally, regarding the South I think some simply won't be able to let go of racist animus, and some kind of reactionary White Power party will always exist. It's just that it would be more or less a national pariah. White Southerners would be divided in thirds: one would be die-hards who, while not able to advocate outright nullification or terrorism, defend the Confederacy and White Supremacy; another would be more "respectable" New Line, the Wade Hampton-kind that seem to accept the new order but still want classism and probably could ally with conservative Northerners; and the final third would be Republicans who would probably go to the Workingmen in the future.
I actually do want to make maps, especially depicting the main military campaigns, but my poor map making skills are not up to the task, I'm afraid. And yeah, the Army of the Potomac sounds better, but maybe ITTL they scoff and say it doesn't have the same ring as Army of the Susquehanna. 
