Bath fan wiring, switch for the fan has been removed to replace with a timer. Switch order is light, heat, fan (L - R). Bath vent has light, fan and heat. Power comes into the box on the left. Check it out.
You guys got it - and the master bath has the same deal. And I've worked on the fan unit using a metal ladder with it "hot". The fix I used was to steal the light wire. We don't use the lights in the things anyway. Plenty of light over the vanity.
I found a similar setup when I worked on the master vanity light. They used the ground wire as the switch return.
We don't take anything to the dry cleaners, so all we have are plastic coat hangers. But now that you mention it there is loosy-goosy barb wire fence just down the alley. That should handle 30A easy.