Joshua Lawrence Chamberlain, the Hero of Little Round Top, could very well won and win for the GOP if the cards are played right.
Huh? what?
Sure he is governor of Maine from 1866-1870, but that seems far out of the way for Chamberlain. Interesting choice though.
More likely that you could get Sherman to run (as ironic as that would be given his opinions of politics) especially as the Sherman-Ewing political machine and political connections would get him there easily.
Hell, John A Logan maybe. Hancock (even if he is a democrat), Garfield is 37, so probably not.
Probably actually going to need to look for someone that fits in with the Radical Republican image though, depending on what Lincoln does.
William Seward would have felt entitled positioned as he was in a successful State Dept.
(Whoever gains the Republican nomination wins the presidency.)
ATL Seward vs. OTL Grant? -- Not a whole lot different; unchecked manifest destiny and carpet bag governments; Seward would have kept the crooks out of his administration, but the Indian Agents would have stolen anyway and Indian Removal (Indian Wars) would not have been approached differently; and the abolitionist minded Seward would not have disciplined the abusive carpet bag government in the South, so reconstruction would have played out pretty much as it did as well.
Boy, replacing Grant with Seward is pretty much, . . . boring; I guess since Grant let the Republican 'political machine' run things for his administration and Seward being a big part of that machine, results in no real differences occurring.
Seward is a diehard expansionist, if anything, besides Alaska he would probably push for British Columbia depending on whether or not Canada unifies in 1867.
He probably only serves one term though given that Seward died in 1872, and that is depending on his health and the stress of the Presidency itself.