well in that case, i'm not sure how true to the story you want it, but...
technically SOLDIER, and the TURKs should both be a part of SHIN-RA since in the FF7 story they are both subordinate portions of the SHIN-RA company. The TURKS and SOLDIER should both be different types of elite troups for Shinra, as should pagoda warriors for Wutai. Wutai and Shinra are both good choices for the war that you are mentioning, as is Cosmo Canyon, as they would be a good neutral faction. If you are in need of more factions, instead of spliting up Shinra (Shinra soldiers, Turks, and SOLDIER) look to other less recognized factions, such as the GI (a group that used spears with bows and arrows almost exclusively, This is also the group that turned Seto to stone during the battle for Cosmo Canyon <FF7 backstory I think it would fit> Also don't shortchange the Gold saucer, even if you didn't like the casino aspect of the game, what better place to have a tournament, not to mention that it has it's own prison/gang community living below it <desert gang/Gold saucer faction maybe> I also think it would be cool to have hyper agressive horses (with added cut, piercing, or couched lance dammage) as neutral enemies in some battles as like random encounter behemoths, just to add a new level of difficulty. Thats about all i have for now let me know what you think