If your spraying so much that the heat doesn't evaporate the moisture, yeah thats not good. But the OP said spray the sides of the container, not the actual egg cartons. A light misting once or twice a day would still be okay as long as it was able to dry out from the heat. But you are right, they don't need to be constantly moist to have high humidity. I've never sprayed my containers and have good breeding success with both species, even the other species which needs super high humidity.

I use all sorts of fruits that get a little too soft, peaches, oranges, watermelon, etc..