Sub-floor trouble in bathroom
You could frame below the level of the rough floor and have the subfloor flush with the joists. That would give you room for 7/16 hardie board, glue, and tiles. (But what a huge pain!)

Alternately, get vinyl and your thickness problem goes away.

I'm concerned that if something as mundane as a floor failed, then what of the shower stall? Isn't it going to have the same (if not worse) problems? If that's a goner, then you don't have a thickness problem any more...