Have you seen this writeup that compares the Revell Kearsarge and Alabama kits? http://www.steelnavy.com/Alabama&Kearsarge.htm
Interesting reading. There's no date, but I think I remember first reading it back in the early 2000s. (Back when we hadn't seen a release of the Kearsarge on the market for over 30 years!)
The author points out that the Kearsarge kit is a mix of 1864 and post-1888 refit features, while the Alabama is a modification of the Kearsarge molds to try to make it look different, but has some serious dimension and shape errors... (The Alabama was 11 feet longer than Kearsarge, for starters.)
The conclusion is that the best way to get an accurate Kearsarge model is to start with an Alabama hull!
As I said, very interesting reading. Even if you're not looking to undertake such a big conversion project, you may get some ideas about simpler changes you could make to Kearsarge to make her look more like the the 1864 version.....