Imo CHE for a 20 gallon long is an overkill. Those things get so hot even with a t-stat. Can you move the enclosure to a 77-80F room temp in the house? That could easily solve that problem. Make sure that the CHE bulb goes to a fixture just for such bulbs.
Your warm spot should be about 88F and no higher than 90F which would be created by your UTH.
Both needs to be on t-stats. The t-stat for the CHE should be one that operates as a dimmer. Not all t-stats are created equally. Most are sold as pulse or on/off which works great with UTH. If you can afford it, I would invest in a Herpstat 2 which will help you control temps for the UTH and CHE separately and it comes with a function choice: dimming or pulse.