Ditch the lamp and use flexwatt or a UTH on the warm side. Drill some air vent holes under the spot where you want the heat, place the pad Inside the cage before it's completed, and cover with vinyl flooring, plexiglass, or tile. That becomes the floor of the cage and the holes underneath also serve as a spot to place the thermostat probe.

That's what I plan to do with the 4 stackable cages I'll be building this summer, and I did something similar with my corn snake enclosure system already.

And since your room is that warm, you don't need additional heat at all for the cool side.