Sourdough bun proofing questions

Hello!

I have a recipe for sourdough buns where I'm looking for help improving my proofing. I'm looking for help in two areas: 1) how to keep dough from sticking to the damp cloth I cover it with for the second proof and 2) what to do while the oven is preheating when I proof the dough in a cold oven with the oven light. 

1) to keep the dough from drying out, I cover it with a damp cloth. But I use shallow pans, and then I pull the cloth off, if sticks to the dough. Suggestions? I'm afraid to leave it uncovered because I live in a dry area and I'm worried about it drying out. It proofs in my oven with the oven light on, because my house is cold.  

2) Because I proof in my oven, I have to take it out before I bake so my oven can preheat. I find it immediately deflates in the cold temperatures. I wait to score it until right before it goes in, but it has already deflated some, plus deformed because of the cloth sticking (see #1). 

Any help is much appreciated. This recipe turns out surprisingly decent results despite the problems I've mentioned. The buns stay pretty flat, but have a good texture. , I can only imagine that it would be even better if I didn't totally screw it up between the second rise and the bake.....also, I wouldn't mind rounder buns!