JUST SCANNED DISK4:
if you reach disk 4 before 12 hours the chance doubles until gameplay reaches 14 hours, also it becomes 4 times as likely, (which isnt that big of a difference) if you defeat the big round guy in air garden. It will not show up for some reason (unless I read the thing wrong which is definatively possible) if both Garnet and Quina are in the party, unless Steiner is also present. It will not show up if you have excalibur 1 equiped or if you own the other excalibur 2. Also, it will not show up if you have defeated the boss immediatly before Kuja in disk 4. Other than that, I dont know. plus, wow I havent ever gotten ultima wepon in any of them, whoever did must play a ton.