Raise the lid daily. Maybe I should say 'nightly.' Let the tub breath a bit. You just want it to cool a little, not a lot.
Letting off that little bit of heat will help with the overheating issue in warm weather. The heat is coming as a byproduct of the circ pump, so letting it out shouldn't raise your cost of operation.
I know it's a hassle, but if you want the circ pump to keep running, you'll have to allow an outlet for the heat. Another way to look at it: if the lid isn't getting opened on a regular basis, one would assume you aren't using the tub on a regular basis. In that case, there's really no need for the circ pump and ozonator to be running constantly.