Correct attic /cathedral ceiling insulation


#1

i am planning on refinishing my attic into an office.

but with 2x6 (an old house with actual old 2" by 6" lumber) attic rafters, it leaves me with little room for proper insulation in my northern new jersey home.

so, i was thinking of extending my rafters with 2x4s.
that would make the rafters 9.5 inches in depth.

leaving 1.5 inches for venting against the bottom of the sheathing leaves me 8" to play with…

i was thinking of using both rigid foam panels AND fiberglass batts.
nailing furring strips along the rafters where they meet the sheathing (to keep the insulation 1.5 inches from the sheathing), and using 2" rigid foam boards - which would insulate and create the baffle. then as much fiberglass that will fit in the remaining space (6 inches or so)

does this sound like a good idea or do i create vapor barrier issue if i’m also planning on using a poly vapor barrier on the inside between the batts and the drywall?

thanks for any help.