An overhead fan is no big deal. It isn't going to make a gale inside your cage. And actually, as long as you can maintain humidity levels, air flow is a good thing!
For humidity, the less ventilation you have the better humidity is retained. Doesn't matter if the walls are PVC, glass, plastic, whatever, if they are impervious to air. The reason glass tanks are bad at keeping humidity is because of screen lids, not because moisture escapes through glass.
If you're ending up with more humidity than you want, make more holes in your tub. If you end up with less humidity, cover some holes.
The problem with spraying for humidity is that it results in a relatively small amount of water on the surface of everything, which all evaporates quickly into the air and then escapes. That gives you a short term spike in the humidity, followed by a steep drop. What you really want is moisture that evaporates fast enough to keep the humidity where you want it, but not all at once; and enough of it that it lasts awhile so you aren't constantly having to mess with it. Putting the water dish on/under a heat source can help. Live plants can help a lot. Even a dish full of soil, peat moss, eco earth, or just your normal substrate (as long as it isn't aspen or something else that can get moldy easily) that you keep watered as if it had a plant in it can help. If you then put a hide on top of that dish, you have a humid hide.
Depending on the size of the RHP, it should have no problem maintaining a good ambient temperature with the A/C on.
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