I understand the situation. Like Kevin said, go the the lumber yard and get some 2x2's to nail or screw full length to the rafters. Usually they just rip a 2x4 down the middle so you end up with a board that measures 1.5" wide by a little under 1.75" which still gives you a tight fit. Your next choice would be 2x4's.
I'm not sure where you are at, but around the midwest, 6" of ceiling insulation isn't enough although it would be better than nothing. I would probably use 2x6's or 8's and then use metal gussets to attach them to your present framing to get an R-30 and consider R-38 if you are close to canada. I think www.jm.com may have some info to help you. Whatever you do, Good luck.