Try soaking him in tepid water for a while and then have him slither thru a towel in your hands. This might help getting the old shed off his belly
As for the uth you need to do one of two things so the burns don't happen again.
Get a dimmer or t-stat for the uth to lower the heat it gives out
Buy a human heat pad ( I would still use a t-stat or dimmer to control the heat it gives out)
Bp's really need belly heat not overhead heat. Do some searches on here and you can find the pic of the heat pads people use ( WalMart) they only cost around 10-15.00
That overhead heat emitter is sucking up the humidity which in turn is aiding to the bad shed
What are your humidity levels? should be around 50-60 and bump up to 70 in shed.
Hope this helps