"I wonder if some of the really early elections are doable"
I looked at these. I have everything written down up to 1868 somewhere.
There are several big problems with 1796 to 1820, which to some extent apply to 1824 as well. The modern presidential election system, in the sense of two national candidates running nationwide campaigns to try to get votes for their slates of electors, really didn't get going until 1828, and that in large part was a reaction to how 1824 went down. Even after that, the Whigs tried running several regional candidates for a couple of elections.
The big problem you have with 1796 through 1820 is the sheer number of states, I think it was most of them at least at the beginning, where the state legislatures picked the electors. This remained the case with South Carolina up to 1860, and in the 1844 scenario South Carolina is just awarded automatically to Polk.
The second problem is that the Federalists were never a really national political party. What popular support they had was limited to New England and the Tidewater parts of the South. DeWitt Clinton may have had a chance, but he was a Republican, who had first tried for the Republican nomination, and the Federalists decided to support him when he ran as an independent. Rufus King wasn't really trying in 1816, and Pickney in 1804 and 1808 never had a chance at all. So the only one of these you could really do is 1812.
The third problem is with the 1796 and 1800 elections. They were held before the 12th Amendment, which legally put in place the system of electing presidents that we still had. The earlier system had the Electoral College, but it really functioned quite differently.
For 1864 through 1876 you really have to change the goal of the Democratic player to make the Republicans resort to as much fraud as possible, on the 1876 scale, in order to win. Maybe you can give the Republican candidate options as to how mcuh fraud to use. For example, for 1864 they created two new states (West Virginia and Nevada) pretty much out of their ---, were planning to use the electoral votes of Louisiana and Tennessee if needed, plus border states where there was a heavy army presence (Maryland and Missouri) went for Lincoln by unbelievable margins. I wrote up 1864 and there are some interesting strategic choices due to the possibility of a Fremont run and the Copperhead plank, also does Lincoln really back the attritional strategy that Grant wound up using?