Like your first plan, I would just cut a hole and put a wire mesh with a CHE lamp on top. Just keep the mesh cut close to the size of the lamp, and heat and humidity won't escape easily. I've seen people do this setup around quite a few times!
You should be letting your thermostat probe hang under the CHE for ambient temp. Put the probe through a hole in the top of the tub and let it hang, is what I personally do for my RHP. The probe shouldn't be laying on the substrate/anywhere the snake can sit on, since if he pees/spills water or sits on it, it won't measure the ambient reading correctly and cause heat spikes.
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