Good luck with this. We tried to use a Heated Blanket when we first started out. I called the folks who installed our system and before I could even get to the root of the problem, he says "Let me guess, you're trying to use a heated blanket?"
From what he explained, most electrical systems have some sort of brain, per say, that tells them how to regulate their power consumption. Heating Blankets, Coffee Makers and Microwaves don't have this. They all just turn on and suck 100% of the maximum watts at all times. So those are the worst things you can use. He mentioned other things like Curling Irons, Hair Dryers and a few other items that I'm sure don't pertain to the Overland World.
I know when I'm in Truck Stops, they offer 12volt Heating Blankets, and I've always wondered if they wouldn't use as much power? Just never got around to trying to experiment with it? Oh, we have a 2000watt Sinewave Inverter and 4 AGM 6-Volt Batteries run in Parallel. It sucked them dry in a matter of 20 minutes trying to run a standard queen heating blanket!
Let me know what you find out