Insulation, Radiant and Vapor Barriers - bedroom over garage

Hello. I have a bedroom above a garage. The bedroom is extremely cold and the insulation in the floor is only 6" thick. The joists are either 2x12 or 2x14 which leaves up to 8" of air. I don't want to spray or remove drywall to re-insulate. Can I warm up this bedroom by either using 1x4 as a spacer attached to existing drywall in garage and on top of it add a whole other layer of drywall? Or would it be better to attach foam sheets to ceiling in garage and drywall over that? Even though I am not eliminating the gap in the floor joist insulation, can either of these (or any other) options significantly warm that bedroom? Thank you for any feedback. Dave

The only way you will make a significant difference will be to fill that 6" void that exists between the joists. That would increase the "R" value from the R-19 that is presently there to R-38. Adding another layer of sheetrock to the ceiling (with or without foam behind it) is just as much work as installing new 'rock after you reinsulate the joists. Just make sure you use 5/8" Type X 'rock on the ceiling. It's a firewall!