New update:

I believe this room to be an unpermitted addition. Based on the fact that A) I know building permits exist for this property back to at least 1914, and I have copies of all of them and B) the construction is beyond awful.

Half of the exterior walls have no foundation - I can stick a prybar through to the outside under the walls. If I can solve that problem, I plan to just lay in a brick floor over sand. Otherwise...I have no idea what's next. At least I know where the rot came from in the corner opposite the washer.