RNG Purgatory until I get the Power Hammer

I'm (I think) now walled off from any forward progress until I can craft the power hammer. In all my runs of the game, I've seen the Workshop appear maybe twice, and I don't have any upgrades to the coat check.

Am I doomed to just spin the wheel until I can craft the hammer?

I've already gotten into the antechamber and used the basement key on a couple of entrances.