Your option is best but you can easily run that romex to a spot behind the heater (inside the MOTOR HOME) in fact if the gas/electric model you buy is a Atwood that's where you need to run it anyway,, install a 15/20 amp SIMPLEX (or duplex) outlet there and plug in the hott rod.. Electric heat normally takes about an hour to recover by the way (heat the water).
IF you choose a DUPLEX. you can drop a line down into the wet bay (Assuming enclsoed tanks) and plug in a string of C-9 old fashion (large size) Christmas tree lamps and perhaps a 100 Watt trouble light.. Plugged in via a T-Stat type outlet adapter (Sold at farm type stores for stock tank heaters) it does a great job of defrosting. (About 10 degrees worth in my case, one string of C-9's and a 100 watt caged lamp in the other end of the wet bay (Caged is in trouble lamp)