I see this thread has been resurrected, so I am going to chime in here as it is a matter of discussion and due to the Texas freeze out last month, something that got a bit of a workout for me.
I have a Zodi Hot Tap instant hot shower, now mind you Zodi seems to be no longer in business since the 'rona so probably not avaialble, but there are lots similar. HOWEVER, I wanted to mention that I already have a stove, and had a battery shower. My Zodi uses a 5 gallon bucket for a water source, I was actually trying to get a hold of Zodi to get the 4 gallon case / bucket for mine which is why I found them unresponsive... but I digress.
So in a situation where 1lb propane bottles ran out quickly, and were unavailable, I was able to use regular unleaded in my Coleman Dual Fuel stove to heat water on the stove, mix it with dang that's cold water in a 5 gallon bucket, and come up with nice steamy shower water in a bucket.
Honestly, if you are measuing every inch, and justifying every piece of gear on your trip. You are I assume already bringing a stove, and some sort of vessel capable of heating water in, and some sort of large vessel capable of holding a quantity of water. I would seriously consider saving the money, and space, and just going with the heat your water on the stove and spray it with a battery shower routine.
It's no slower than a propane shower, it takes a lot less space, and I mean a LOT less space, it is less to maintain, fewer things to break etc... doesn't require a dedicated fuel source etc...
You can heat your water over a stove, over the campfire, or....
Use a solar shower bag to heat your water, empty the bag into your vessel and pump from there. I HATE lifting 5 gallons of water overhead. You are free to but I don't wanna...
Of course if you are travelling with a partner that can / will help, it MIGHT be worth it to do the shower bags. Just lay one per person out, and the both of you can haul it up to let gravity do its thing.
