I am working on a house with an addition which has non-ventilated roof over a crawl space.  The roof in the addition has open trusses for visual asethetics and the drywall butts up to these trusses.  There is however small gaps in places where you can see the insulation and truss brackets.  Currently I am working on wrapping the rough lumber trusses with finish lumber, but some of the insulation is damp and the roof trusses are damp.

I think what is going on is water vapor is traveling upward into the cracks in the drywall, basically going to the highest point possible and then condensating when the roof temperature (or truss brackets) reaches the dew point.

My question is if I dry the area out with a fan pointed in the cracks and then put my finish lumber up and seal it real good will that keep the water vapor in the room and prevent it from going up into the insulation? 

Also is it possible to get the insulation completely dry? 

If water vapor does get into the roof insulation is it going to become moldy before it has a chance to somehow find a way out?

Is this a recipe for disaster with moisture condensating on the backside of the finish lumber and ruining the finish?

Thanks in advance for your input!