This is a tough one. I'm starting to wonder if it's actually the camper, or something else you use while the camper is loaded. Do you have a backup camera or anything you plug in inside the truck that you only have hooked up with the camper loaded? You did say with the camper unplugged you don't have this problem. Was that with no other changes than the camper plugged pulled or was that with the camper unloaded and maybe something else also disconnected in the cab?
The truck's computers are supposed to go into a low power mode sometime after shutdown. But I have a bluetooth OBD-II reader that apparently keeps mine active and will kill the batteries in a few days if I forget and leave it plugged in.
Not sure if/how this could happen, but check if you have any stray voltages on the camper side of your plug. Maybe a stray voltage being back fed into the truck is keeping some electronics from going into low power mode?
Just throwing out ideas, just in case. You've covered the obvious stuff. Now it's time to look for the weird. :)