I think you just answered your question about why he's in the moist hide. It's the best temp for him.
73F is way too cold for anywhere in the tank for a BP. 75F as well. 90F is great for when he needs to digest, but the rest of the time, he wants low - mid 80's. In 20L, I imagine the moist hide, sitting in the middle of the tank is where he wants to be. There is no hide there, so he uses the moist hide instead.
You need to fix temps.
I would move the CHE closer to the right side, get a second one, or get a UTH for the hot side to make his hot spot and move the CHE closer to the right side. ALTERNATIVELY, get a UTH for the cool side and set the thermostat so the cool spot is 78-80F.
I assume you are using a thermostat on all your heating elements. If not, you need to.
Secondly, how are you reading temps? It should be with a IR temp gun on the ground where he is/would be.
Keep us in the loop, but I think the mystery may be solved.