How to finish closet ceiling in garage space
Long post warning!
Due to a frozen pipe, I was in my mom's garage's attic (abuts her house, shares a common wall). In drawing (just learning google sketch), there is an inside closet that intrudes into the garage. Thick black line is garage ceiling plane. That closet has a heating duct running in it; the ceiling of the closet is drywalled beneath the duct space. In the garage ceiling, the space above the duct space was only "sealed" with faced insulation. I think it should be for fire protection (no way to stop fire from entering duct space from attic space) and to reduce air infiltration (This is what caused frozen pipe: there were 6 of the 2nd floor joist bays open to the garage attic space, one of which had the pipes in them).
So, my question: What should I install from the garage attic space between the joists that lie above this duct chase? I can't install from below unless I rip out the closet ceiling but then I'd have the duct work to contend with.
One limitation: I've about a 2' x 2' ceiling hole to access the garage attic.
Should I cut drywall to fit between the joists (whole space to cover is 36" x 62")? I'm a bit concerned about drywall sagging since I can't install it to the bottom edge of the joists; I thought about running a 1 x 3" flat alongside joists to support drywall edges. Agree?
When done, I'll spray foam gaps where drywall hits joists with fireblock foam and then insulate with fiberglass batts.