My garage has a vaulted ceiling on 2x6 joists. The main roof of the building is a bit above it and the vaulted ceiling is not covered with any sheeting. I could feasibly put 2x8 batts of insulation in the cavities and then sheetrock it up. The insulation would stick out 2" or so above the joists. Would this achieve me any better R valve? or should I just use 2x6 insulation and call it a day. Thanks in advance.
Compressing insulation designed for 2x8 into a 2x6 cavity will yield a negligible R-value difference.
You can buy R-21 insulation for 2x6 cavities but if you buy R-30C then it will only be worth R-22 once compressed.
Insulation is a delicate balance of air space and fiberglass. Air is a terrible conductor of heat.