Well, I just noticed one thing. The thing I have marked as portrait is NOT portrait. I'm not really sure what it is. There are a few things I noticed about it.
1. If it's duplicated, the first person to have it will be not in battle. The HP and MP will go to 0 although the character won't be "dead" and the other two characters will perform the battle as if the duped character wasn't there.
2. It has something to do with limit bar. If the numbers are swapped with another character then their limit bars will swap IN BATTLE, but not in the menu.
2a. Extending this line of thought, it MAY affect limits learned and times limits have been used.
2b. Might also affect number of kills, but I haven't tested either of these yet.
3. It doesn't affect battle names, equipment, materia, stats, or the limits themselves.
4. The characters look the same with any value so it's not battle model.
5. Every character has a unique value at this location.
I have no idea what this is. It's almost like character ID rather than portrait (which I think is determined in the menu files rather than the kernel). But since the equipment and materia doesn't change I can't say for sure.
I tested this out by switching Tifa and Aeris's values at this location in the save games.