It turns out I fixed it in the meantime and my solution was basically the same idea.
I wasn't sure if fooling around with the LoadClass routine would mess up something else, like the actual battle sprites or something, so I looked for some code in that bank that I could cut, and found it in the form of the palette cycling (there was a surprising amount of code dedicated to that and all it did was slow the gameplay down). Essentially, killed two birds with one stone!
Anyway I made my own subroutine that was more or less a copy of LoadClass except it only loaded a single row of battle graphics, then called it for each job, resulting in the first row of all 12 jobs being loaded next to each other. I also modified the job rotating routine to only move by one row instead of two when changing jobs in the party creation menu, and that did the trick. It looks perfect now.
Huge thanks to everyone for their help! Ever since I began experimenting with the 12-job setup I was always disappointed that the character select graphics wouldn't work out of the gate, and I was always sad that I never had the skills to really deal with it myself, and was always apologizing for how it looked and how it was only that screen that looked bad. Now it looks great, and seamless! No more apologizing necessary. I'm still gonna give the game another once-over to clean up any other possible cosmetic / minor details and then release the new patch hopefully soon.