Nice one; I was considering doing the same kind of run, though my thought was to use a Tinker. A rogue on one of the easy levels where the enemies are all that much weaker makes a lot of sense, though. I agree with you on "feeling parched", though a badge for curb-stomping the dungeon is perfectly fine in my books.
I also agree that the old Cheeky was more interesting than the new one. I'd much prefer the two alternatives you mention; those would be much more in keeping with the difficulty of the harder badges like hoarder or purist. Unstoppable is a bit underwhelming, but there is something satisfying about clearing the dungeon so I think it's definitely worth having the badge. Now Ding! Max is very underwhelming and quite possibly the easiest badge after cheeky, and for Assassins it's essentially redundant with Unstoppable anyways...