Personally, I question your battery lasting the night with the furnace on. I also question your truck recharging your battery between camping spots. You have a good start with the LEDs.
My suggestion is use the small propane heater. I have used the stove (burners and/or oven). There will be the nay Sayers, but it is no different than cooking and baking. I would not sleep with them on.
Easy for me to spend your money, but strongly suggest a
Olympian Wave 3 Catalytic Safety Heater (about
$209.49). I have had them for many years, and it is my primary heat in my current TC. They use only propane, and can be used as a portable heater.
Wayne