I definitely would second that. Yes, you can run a high-gauge extension cord through the same mousehole as the electric cord in some rigs, so you can use that for one 1500 watt heater, then use the receptacle for another... but realistically, I would recommend getting the furnace fixed.
Yes, it uses propane, but a 1500 watt heater is not going to do much in a larger rig, other than be supplemental at best. I learned this by trial and error.
As an alternative to the furnace, perhaps consider a vented platinum catalyst LP gas heater. Key word here is vented, where the combustion gases are exhausted safely outside.
Another alternative is to toss the furnace and water heater, buy a Truma Combi unit which works on electric, LP gas, or both. This way, you will still use propane, but it will use 1500 watts from electric as a way to lesson the fuel usage. Another advantage is that it frees up a lot of space because one appliance does the work of two.
As for electric heaters, I personally use Vornadoes. I have an older model when they were made in the US, and it does quite well in circulating warm air throughout the RV.