In case anyone is interested, I wanted to give you an update:
I went ahead and got a 40W radiant heat panel (the old was 120W... yikes).
I hooked it up to the thermostat and set it to about 93F (1-2" under the surface of the RHP). The first problem was it wasn't strong enough unless the temperature in the room was 80F+. Then, when the temp was that high, the whole tank was too warm (84F on the cool side).
So, I had to build up the substrate on one side of the tank about 4" higher than the other side, using driftwood branches to contain the extra substrate. For the cool hide, I use a corner hide that can be butted up against the glass, and with very little substrate on the ground, and build up a little mound of substrate around it - with the intention to further insulate the cool side hide from the heat. Not sure if that is making any difference.
With the warm hide that much closer to the RHP, I was able to lower the RHP and create a better temp balance. The cool hide is now 79-80, inside the warm hide is 88-90, the top surface of the warm hide is 90-92, and the ambient temp is 80-85. He is using both hides, and I'm happy with the new setup, knowing that even if the thermostat fails he is at pretty low risk of overheating even with the RHP at full blast (at least, not quickly) and at no risk of burning. Also glad to cut down on wires and potential failure points.