Yeah, this one was a pain for me.
Here's what I ultimately won with after I decided "okay forget using Bond CEs and the teapot - this quest needs to go"
Front Line: Suicide Squad - Habetrot/Arash/Chen Gong. They had one job and one job only - fire all their NPs Turn 1 and die in order to cycle the enemy classes and soften them up a bit since they lose some resistance every class change. Careful on the NP order (I went Arash-Habetrot-Chen, but really just avoid an "oops" by having Chen arrow someone before they have a chance to use their NP)
Back Line/"The Real Team" - Castoria/Lady Avalon/Summer Erice (NP2, Level 90, Black Grail, non MLB) - they roll in Turn 2 and the real fight begins. You should be looking at Himiko/Hyde/Saber Lily. Drop all the buffs on Erice and nuke Hyde because his passive is obnoxious. Ideally Erice can card her way back to being able to NP but mine didn't so I just dropped a Command Seal because I was so done at this point. Next up is Himiko - she got blasted for about 950k which isn't quite a kill but easily puts Salieri into kill range for the next NP. That was 3 turns so all the buffs dropped and I just waited it out until they came online again and blasted Lily a few times until I won.