Plans I have for one of my TLs if I ever redo it, for the American Civil War to last longer:
1. Due to better British success in the alt-war of 1812, they take New Orleans. The US gets it back in the peace (which had already been made), but the perceived threat against New Orleans means more fortifications are constructed there and a small naval station placed there, with associated small industries to repair and maintain steam engines for the navy.
2. This naval station (after a brief inter-fight) sides with the Confederates meaning the south has a (very) small navy and the infrastructure to maintain it. It also has a decently competent commander.
3. The evacuation of Norfolk is even more panicked and botched, and the CSA captures a couple of ships almost intact and a lot more naval supplies.
4. Farragut comes to take New Orleans 1862 and run into actual mines when yelling "Damn the torpedoes!", he is killed and most of his squadron sunk. In the ensuing panic, the union abandons Fort Jefferson in the Florida Keys to the CSA navy and abandons several forts and sieges south of North Carolina. It takes until 1863 before the Union gets its act together and starts to move south again and they retake Fort Jefferson in 1863.
5. Someone competent, perhaps Judah P Benjamin is in charge of the CSA treasury. The south actively avoids King Cotton and sells as much cotton and other produce they can get through the blockade (which is non-existant in the Gulf of Mexico until late 1863 due to the earlier changes) and avoids most of the ruinous inflation of their currency. Benjamin will be attacked as a "niggardly Jew actively hindering the war effort" by the southern press and will be forced out by 1864, and inflation will take off as the blockade tightens.
6. Since the supply situation is much better, especially in the west, and the US can't use the Mississippi as they did OTL, the going is much slower, and the ability of the south to use the lower Mississippi as a transport hub allows them to use the troops of the Trans-Misssissippi Department much more, which further slows the US advance down the Mississippi.
7. With strong CSA forces along the Mississippi and in northern Georgia, both better equipped and supplied than the OTL forces, Sherman can't break away from his supply lines and march through Georgia in the same way.
8. With the CSA beign better supplied, having better internal communication and a better economy compared to OTL, the distances and the fact that the US has to conquer all of it from the north, combined with the distances and supply issues means that the last CSA army, probably the Department of the Trans-Mississippi fighting around New Orleans does not surrender until early 1867.