They should redo their current set first, and it would be nice in some instances where there would be an option to run the runner-up for the nomination instead of the historical nominee.
"Elections I'd like on here, in order of preference: 1912, 1992, 1980, 1876"
I tried doing write ups on each election, assessing their suitability for the Campaign Trail treatment, this summer, and got stalled with the 1876 election. I hope to resume them, but there is a big problem with the four elections between 1864 and 1876, with them becoming most acute in 1876.
The big problem is that the Republicans were simply not going to let the Democrats win any of them, and absent an unlikely Democratic breakthrough in the northern states (the Democrats in fact made it close in 1868 and 1876 by winning New York), could use their control of the reconstruction governments in the South to prevent this. Even in 1864, they were prepared to seat Republican electors from Louisiana and Tennessee if needed, though they turned out not to be needed. There were suspiciously large Lincoln majorities in that election in some of the border states that were effectively under military control.
Another thing the Republicans could and did do was to create instant states out of low population Western territories, which they did throughout the nineteenth century. Examples were Nevada in 1864 and Colorado in 1876, and in Colorado the electors were not even elected that year -Tilden won a majority of the electors chosen, however notionally, by the voters. The point is that they could always see how things were going in the North, some states voted as early as September, then bring in as many new Western states or tighten things up in the South as much as needed.
The crooked 1876 agreement ended this at least as far as the Reconstruction governments were concerned, in return for conceding the White House for another four years to the Republicans. So 1880 was the first election in decades that either party could win, and it turned out to be close. This election would be good for the scenario.
For the 1864-1876 elections the best you can do as the Democrats would be to run well enough that the cheating would just get out of control, forcing the 1876 deal. And despite the historical myth to the contrary, 1864 was a non-starter as soon as the Copperhead plank was adopted.
For the others, what is attractive about 1912 and 1992, the strong third party runs, also makes them really complicated. I don't think the system does third party candidates well when the candidates control them and they shouldn't try. For 1912, I think Roosevelt should be treated as the alternative to Wilson and Taft as the third party candidate. For 1992, I don't know how you create a system to model Perot's erratic behavior, and I don't think any player would willingly do it.
My list would be 1828, 1880, 1940, and 2004, the latter because it would complete the 21st century set.