"Don't try this at home" - everyone told me it wouldn't work, would burn down the house, kill me with carbon monoxide. whiteboard wouldn't do as it'd rot or sag - even though it doesn't get wet.. Well, nope.
I got a small propane on-demand heater intended for camping (who the heck needs that - some new definition of camping?). Cheap stuff, but careful installation and don't twist off the connectors and it's good.
A friend, Jeremiah, came over and installed it with some whiteboard Bill had brought me. The quick coupling for the shower head was drippy at my line pressure, so I installed a ball valve, mostly because it was not dissimilar metal and was F-F npt - and a nipple and hose clamp instead of their arrangement - not one drip.
The CO monitor (another donation from Bill) I put in the room didn't go off. Because "everyone knows" it's going to burn the house down - despite being an on the spot fire extinguisher...I used the thermal camera to take some pics after a good long wash. Heh. It's efficient, most of the energy goes into the water, as it should. Only the exhaust port gets actually hot.
Here's the thermal pix.
And the unit. Of course, the clock in the camera is way off...as is the registration between the visible and IR. But it was cheap!
Here's a link to the unit on Amaon.
The reviews about the crappy shower hose can be disregarded, they fixed it with a better one. But the quick coupler for the output leaks like a compressed air fitting (which it's a copy of).
Can't have that, so I added the ball valve and a real hose nipple and clamp.
So, after some years having to make sure I had surplus water, and surplus electricity, which rarely happen together...now I can wash my sorry butt pretty much anytime. This doesn't waste water or propane.