Vaulted Ceiling Problems

[cntrlmn95]

I have a vaulted ceiling that continues to cause humidity problems during the summer months. I've had it looked at by 2 insulation company's and both agree that it is insulated and sealed properly. Problem is during summer months the return vents will drip water when the humidity is high. Last year i purchased a portable dehumidifier and it solves the problem but it is not pleasant having this unit running all of the time. My question is would it cause any moisture issues if i put down either foam board insulation or plywood over this vaulted area to keep the humidity out of this area? I've attached a simple paint drawing to kind of show how the ceiling is configured. Any ideas will be appreciated.