The screen lid + the heat bulb is what is making it impossible to keep your humidity up. There are a few tutorials in the sticky section on how to modify your screen top to trap more humidity. I just like to do a sheet of plexiglass over most of the screen. You do want some ventilation though. Moving a deep water bowl closer to the heat bulb should help create a bit more humidity.
Once you've soaked the snake, you can peel the skin off with your fingers. I sometimes use a damp paper towel to help "roll" the skin off front to back. The longer you let the snake soak, the easier it is to peel off.