I think the interesting challenge will be making it feel like the Civil War. This means the north has to have the advantage, but the South can't fall quickly.
My thought would be to give Great Generals a huge boost and give the Confederacy a couple (i.e., Robert E. Lee, Stonewall Jackson, etc.). The north would have to earn one through combat and eventually generate one (Ulysses S. Grant, of course). The Confederacy would also get combat bonuses when near a GG and on their territory, but perhaps less so on enemy territory. The north would also get massive production bonuses and a rail network to quickly move them to the front. Essentially, the north will always have number advantages, but the south's troops will fight better. This changes as the north gets Grant. The north can also try and take cities elsewhere where Lee can't fight.
I would also have an asymmetric victory condition. The north needs to take Richmond and maybe a few other cities (I require all cities, though). The south, on the other hand, just needs to create war weariness. Maybe have an election or some kind of time moment and the war weariness has to be under a certain amount. Union casualties raise it, capturing cities lowers it. Even more war weariness for victories on Union soil where the Union will have the advantage.