It took a lot of trial and error, but I finally managed to Champion elite Red Dragon without using a mythril refresh!
Here was my loadout aka
TEAM STATUS EFFECTS:
http://i.imgur.com/opHFcMZ.jpg
Slow + Blind + Poison made it so that the only real threat was Southern Cross. When Red Dragon cast the first Flare, I used Magic Shield, went into burst mode, and hoped for the best. Flare Star was mostly manageable, but Wakka's RES was so low that he wouldn't survive it if he wasn't already at full health. I went with Retaliate, but it is by no means required here.
So really it boiled down to a lot of S/L. S/L if Blind & Poison didn't stick on the first round, if Flare Star came out before Magic Shield was up, etc. The most frustrating outcome was when a perfect run would get ruined by Southern Cross at the end--happened 3 times.
Even still, going after this has been a lot of fun