First off do you have the heat pad & heat light connected to a thermostat? If so are they connected to separate thermostats? The belly heat is more important than the heat from the light and should be on all the time between 90-93. A heat light should only be used if you need help getting the ambient temps up. If you do need a heat light get a ceramic heat emitter... As youve noticed the heat lights kill your humidity... A CHE works very well for providing heat w/o killing humidity too bad. Again all heat sources need to be connected to thermostats... To be honest your best bet is to switch to a plastic rubbermaid tub. Youll have no problems with humidity and the heat pad on the bottom is usually good enough if the room the tubs kept in isnt too cold...
As far as helping with the shed... You can go with the damp warm pillow case method or wet wash cloth snake through the hands trick haha... Check out some previous threads and youll see theres much information on your situation. Welcome to BP.net and good luck with the new guy!