I'm not sure, I think Battle Square doesn't display it but I'll bet that it's hard-coded in some way and can't be used elsewhere (could try using it's Battle Mode but it's a long shot, I think it might actually force the Battle Square background as well). The Yuffie Pagoda fights also display Game Over if I remember correctly, so the answer won't be there either. I guess the only way is to re-word Game Over to something more ambiguous but you'll still be counting on the player not gunning for that reset button the second their team is on it's last legs.
A more drastic way is informing the player that it's not a game over if they lose, but that's a tension killer.