Can water heater run while towing? Here's why . . .

I'm going with old biscuit's heater pads, or TenOC's light bulbs and heater fans, but only if you decide that Lantley's "why bother" isn't the answer you like.

I'd try to find some 12V heater pads and a way to power them, instead of running what is effectively a tankless water heater recirculation line from the fresh tank out and back. If I understand what you plan to do?