Disclaimer, I'm not a builder or contractor of any type.
I would either do a proper vented roof, or spray foam so their is no air gaps or flow. (cheapest I would think)
I did have to repair my roof because of rotten sheathing & rafter's. More than half of my house is vaulted. The space between the bottom of the plywood sheathing and the sheetrock is 7.25 inches (2x8 rafters.) After tearing my roof apart I concluded that it was originally completely filled with fiberglass bats. The roof has eave vents and ridge vents. No air was flowing, rafters and plywood rotted. Previous owner replaced roof, attempted to sister the rafters and replaced fiberglass with hard foam. Although he left an air gap, he did block off 2 runs where a skylight was removed and also short circuited the ridge vents by installing a ridge vent on a lower peak. I buy house, 2 years later I had water coming in and a sag in the shingles in between the rafters that had the skylights. I open up the sagged area only to find that the rafters had rot from the past. I had to rip up the whole side. The guy used 2x6's to sister 2x8's. I cut out the rot on the rafters and replaced all the 2x6 sisters with 2x8's, replaced all plywood, and rebuild 2 chimneys. I removed the ridge vents because their wasn't enough ridge to get the proper amount of venting and added a power vent fan.
You don't want this.
