I am putting up a drywall ceiling in my basement. The support beams are 2by10. The top hat is about 8" above the drywall. On the directions it says leave 3" of space above the tophat for the heat buildup. I only have an inch and a half or two at the most. Can I still do it?

I would use IC rated cans. They also make "short" cans, about 6" deep.
Oh yeah, I know 2X4's are 1 1/2" X 3 1/2". A 2 X 10 might be 9 1/2" X 1 1/2" still not a problem