On the old CRVL forum I had designed an on demand propane hot water heater system that would circulate hot water thru a "PEX tubing" single zone, run on the floor under the flooring/carpet. It used a Toyota Prius electric water pump connected to a Bosch relay that was triggered by a mechanical thermostat. (and connected to the house battery)
When the temp got low enough the thermostat would trigger the relay to close and energize the electric water pump to circulate coolant thru the water heater which would sense the flow and ignite. As the hot coolant would circulate and heat the floor in time the thermostat would sense the upper limit of heat. (the temp the thermostat was set to maintain) and break the relay's contact with house power....and thus shut down the water pump causing the hot water heater to shut down). This would provide for cyclic heating similar to a house with a boiler and baseboard hydronic heating.
The pump doesn't have brushes and is a sealed unit, capable of a long life.
The main thing is venting the propane water heater to the outside and there should be some provision for expansion of the hot coolant. (like a small tank) I would also suggest some consideration be given to a vent to allow outside air for the burner of the water heater.
The floor would have to have 2X4's secured to it in a manner for the PEX tubing to run thru it like a maze such that the pump pumps the hot coolant into the zone (maze) and the cooled coolant returns to the inlet of the hot water heater.
(pumps tend to push better than they pull) The elevated flooring may have a couple of long narrow metal grates that can be opened or shut (when not needed).
I've thought of a few other ways of doing this but I think this would be the simplest way to go.