I would not use a UTH or heat tape under ceramic, as my understanding is that both need to be able to breathe a little bit in order for trapped heat to escape. Hopefully someone will chime in to correct me if I am wrong. You also don't want to put the UTH's thermostat probe/cord inside the enclosure.
Have you tried just the lamp or just the CHE? CHE needs to be on a thermostat. I personally use dimmers with my lamps, but many advocate for thermostats for lamps as well.
CHEs and lamps do dry things out. A substrate that retains water can help, but I have to mist my enclosures that use lamps, and I also invested in a room humidifier.
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