Ditch the lamp. It will kill you only slightly less in the plastic setup you mentioned.

Is the screen closed off with anything?

Paper towels play a negligible part in your humidity problems - you'd see the same results with newspaper and given the use of a lamp probably only slight gains with barklike substrate.

Do you have a humid hide?

As a stopgap solution if you find a $9 heating pad, jack the tank up off the surface (table, whatever) so theres airflow below and use that until you can find something more applicable.

On the bulbs - what kind of lighting are you trying to provide or why?