Hmmm. . . well, the only thing I can think of is that my dance! tactic was somewhat of a last resort - I discovered it by mistake when I had ran out of anything else to throw at Neo-Ex-Death (my MP was gone for summoning, all my money had run out, etc.), so, out of desparation, I used dance, and it worked really well. My other characters were equiped with weapons like Excalibur, the Brave Sword, and other rare powerful weapons, so that may have helped. I was really surprised that it worked well.
It is possible that because I had already done quite a bit of damage to Neo by double summoning Bahamut and Meteor and the like, that he was weak enough to suffer greatly from being hit with sword dance multiple times. All I know is that it was dancing that allowed me to ultimately win, and I saw those little 9999 signs come up on the screen. I'll have to look back at my saved game to see exactly what I had when I went into battle. Hopefully that will help.
And for future reference, I'm a girl.