Making rafter bays deeper for vaulted ceiling insulation – GreenBuildingAdvisor

Hey guys, I have a dumb question and I have looked it up but getting mixed reviews on how to do it. I am vaulted a ceiling in my house that currently has 2×8 rafters. (I have a roof thats only 6 years old so adding foamboard outside isnt an option). I have a vented roof/soffits/ridge etc and I want to keep it that way so I dont want to spray CC foam directly to roof deck. I am adding venting baffles lets day 2″ deep to each bay from the soffit to the ridge. My 2×8 are actually 7″ so that only leaves me 5″ left for insulation UNLESS I deepen the bays.

Im not a huge fan of covering the whole ceiling with 2x4x8 panels, then drywalling to that… I know its a common thing but it seems like I would get a lot of nail pops etc. I dont know, just doesnt feel right.

I thought I had more space in the bays and planned on doing 3 to 3.5 inch of foam on the baffles and 3.5″ r15 batt for a flash an batt set up to save some money and put me around r35-39.

I can still do this but I need 2 more inches of depth.., or 1.5 inches if I do a 1.5″ vent baffle instead of 2″ (I have to research these more).

Maybe I could find a 1.5″ vent with 2″ spray foam and 3.5″ batt but that would only take me to about r29.

If I added 2×2 (1.5×1.5) furring strips to the bottom of the rafters running parallel with the rafter (essentially just adding 1.5 to the bottom of possible?)… could I use some liquid nails and screws, or do I need to run them across? If I go across it kind of defeats the purpose and I dont have the straight depth that I need.

I know its a beat up subject and I do apologize.

Located in Southern New Jersey for reference. Zone 4