Ours isnt a permanent fixture so is removed from the truck and put into storage ..Emptied and Allowed to warm up to room temp, wiped dry inside, then given a light wipe over the insides / wire bin included with vanilla escence, the lid is held open with a couple of erasers from the kids pencil cases .
Never had a problem yet in 15 odd years .
We do the same, Ours lives in the back of the Cruiser, after use it is wiped dry, then with Vanilla Essences. The lid is then left open a couple of mm's to allow air in. This goes the same for the 3 Way Fridge in the camper. This also, I believe helps with the seal not being squashed and flattened.
Theins, you mentioned that you can't leave the lid up, can you leave it just a couple of mm's maybe?
Or you could do all the above before storing it again, probably a pita if your camper sits outside in the weather.
Vanilla Essences is a big help in reducing mold from forming.
See how you go with that.