Old house challenge with unvented cathedral ceiling (rigid foam on roof, batt insulation interior) – GreenBuildingAdvisor

I’m working on an unvented cathedral ceiling with 4” of polyiso insulation on top of the roof and fiberglass batts on the interior in the rafter bays (one of the recommended “cathedral ceilings that work”: https://www.greenbuildingadvisor.com/article/five-cathedral-ceilings-that-work)

There’s a catch: the sheathing sits on top of some old 1” furring strips that run horizontally (left behind after some cedar shingles from ages ago, I imagine). See the attached images.

If I put batts in that attempt to fully fill the cavity depth-wise, they’ll rest against the furring strips and may or may not fill the gaps between the furring strips. If they don’t, there will be a 1” gap in much of the surface area between the sheathing.

a) Do you believe that the batt insulation, upon compression, would fill the gaps between the furring strips and touch the sheathing?

b) If they don’t, will this materially undermine my ceiling performance (knowing that I have polyiso on the roof)?

c) Is there a creative solution you’d recommend? The polyiso on the roof is already in place and fixed.

Thank you,

Luke