Currently have open frame cathedral ceiling with aprox 7" exposure on the beams. I think there is approx 6-8" of air space between the ceiling and roofing material, but I am not sure. I need to insulate the ceiling but I only see 2 option each with it's own problem(s):

1: Use rigid insulaton to insulate between the beams and cover that with (something). Problems- what to cover rigid with and how to attach it, cost and, near as i can tell 2" of rigid will only net about R-13.

2: Attach 2x's to beams to attach drywall to and insulate between beams with fiberglass insul. Problems- mainly, I will loose quite a bit of exposure which on the beams.

Any thoughts or suggestions?