I FINALLY got the SOB last night!! I used a combination of SeeDRankLou's and NotQuiteNecessary's tactics. I used Rikku as an Alchemist and Yuna and Paine as my Dark Knights. I had Rikku equipped with Auto-Haste, and I used Darkness on EVERY turn with Yuna and Paine. For Rikku's first round, I had her mix a Star and a Light Curtain, which gave me the promised Hi-Wall effect.

I cannot even tell you how much Hi-Wall saved my ass.

I used a Mega-Potion from Rikku's Stash every round thereafter, X-Potion when someone was in really dire straits, and remixed Hi-Wall every time A.M. cast Dispel. I also snuck in a Stamina Tonic in there when everyone was healthy so the party's HP was doubled. That seriously helped.

As long as you've got a mastered Alchemist and all the necessary items, this strategy is very nearly foolproof. And I didn't even have to use my Cat Nip. (Well, I did use it, near the end of the fight...I switched Yuna to Gunner when she was at 3000 HP and yes, the Cat Nip worked...but sadly, it was too late and I was at the very end of the battle. D'oh! )

Thank you SO much to the both of you for your suggestions! I haven't had this much of a challenge since Omega Weapon in FFVIII.