Years ago, I converted a wood cabinet to house a gopher snake, but the floor was much too thick for heat to rise from underneath using UTH. While I've mostly used Flexwatt UTH, at the time I also had some zoo-quality thick ceramic heat pads (another kind of UTH that heats much stronger & is made to safely withstand moisture, as when buried in zoo exhibits). I made a wood square that formed basically a flat-tunnel with wire mesh on top, so the UTH could sit on top- on the mesh (heat easily going up or down thru the wire mesh) & with doorways in 2 wood sides for the snake to pass thru. He could get on top of the heat, or enjoy being underneath it. Just a thought, if you can make it work there. The trouble with the typical heat tape (incl. Flexwatt) is that it's not made for moisture or for being inside the enclosure.
Anyway, I have no pics so I hope what I described makes sense? When you mentioned a "false floor" that reminded me of when I've done something similar.
Another way to heat this takes thinking outside the herpetological box when it comes to supplies. I've also heated a tall cabinet with heat cables- the type they sell for plumbing, to prevent pipes from freezing- and it was hooked to a thermostat- it worked quite well from within the cabinet. They come in various lengths. Just saying.![]()