I've given this a little bit of thought over the years, so here's my two cents:
The lower shear rail on the model appears to be in the approximate location of the original cap rail, which formed the top of the gun ports. You could cut the bulwarks off at the top of the lower rail, except towards the bow where the forecastle deck was, and let the lower rail act as the new cap rail. However, as the shear of the ship was straightened in the 1870's when the bulwarks were raised, to be really accurate you will need to reintroduce the curve back into the shear line, about 8 inches lower at the centerline than at the stern according to Roberts' research.
Whether you decide to correct the shear line or not, there are several other modifications that need to be made to the hull. For one, the kit hull has too many gun ports. The 1864 Kearsarge apparently had only one broadside gun port between the two rectangular pivot gun ports, not three as the kit does, and two, not three, ahead of the forward pivot gun port. In addition, much of the other hull detail, such as pipes and plates, is probably not accurate for 1864. Unfortunately, once you fill in the extraneous gun ports and remove some surface details you are going to have major discontinuities in the kits raised planking detail. This will be difficult, if not impossible, to replicate.
If it were me, I think I would probably start by filling in the open broadside gun ports on both sides of the hull. (You also need to check the locations and sizes of the pivot gun ports as they may have moved when the ship was rearmed in the 1880s. Hopefully they did not, but if they did you will have to fill in the open ones on the starboard side.) I would then remove, by sanding and chiseling, all the raised detail, except the headrails, above the waterline. If you decide not to correct the shear line you could leave the rail molding, but if you are going to correct it I would remove all the detail. Once you have a clean flush hull you can plot and cut the new shear line and then locate and cut the gun ports you want to open at the correct locations. If desired, prior to cutting any new holes you could scribe in the planking runs to retain some of the appearance of the original detail (you're an airplane guy so you might have some experience with scribing).
Not easy nor for the faint of heart. Good luck.