Funkyness..
May seem like a dumb question, but are you on Disk 3? The final battle in the Square is against Proud Clod, and as you don’t fight the actual boss himself until the end of Disk 2, it probably means that you can’t access the special battle. I can’t think of any other reason than that…
As for the problem: weird. I don’t know. Is Omnislash enabled on Cloud? I’m pretty sure you have to enable it on Cloud before you can do the special battle and I think that you have to have it set as his current limit too, but I’m not sure on that one. Oh, and you shouldn’t need 64,000 BP. The special battle should be available any time after you have those two, regardless of how much BP you have. Otherwise, I don’t understand. Your game is wacky.
Edited to respond to Vivi: Cloud is the only person who can participate in the special battle, but he’s always in your party, so that couldn’t be the problem.