Im not sure about resting a rhp on the screen.
For the setup you're going for a dimming tstat is going to work best. An on/off style is going to shorten the life of the che and not give you as consistent numbers.
Many people that have not found the che to work well and complain about them burning out often use the wrong style fixture. The double dome will work but I prefer the wire basket style that is actually for a che. The issue is the che creates so much heat that when it is used in a enclosed dome fixture the heat builds up at the base and burns out the unit. Che's are not cheap but can be if you can make them last. I would look into the wire fixture since they are cheap and could save you a lot of money in the end.