Martyr Wraps are just another niche item you don't want to unlock. They start you off with 3 corrosion, but grant you corrosive strike.
Also, I believe they are going to either buff the monk or weaken the dungeon cause' right now this is EXTREMELY HARD!
(Another alternative which could kill two birds with one stone would be revamping Taurog in a way where he has a way to bypass physical resistance.)
For now, if you want to unlock the Martyr Wraps and you're sick of that red flag, beating the dungeon with anybody completes the quest. (Unless they fixed the bug) I recommend Bloodmage (Use physical attacks, whupaz and blood pool on SMM), Paladin (Convert HALPMEH after SMM destruction and fireball Tower of Goo), or Sorcerer (As someone else mentioned above).
I speak chaos.