Hi –
Background – I am finishing my basement in zone 4 (Southeastern Pa).  I am attaching 2 inch thick foamboard to the poured concrete foundation walls and frame in front of this.  For the rim joists I am using a combination of 2 inches of rigid foam with canned foam sealant placed around the edges and rockwool unfaced behind it.

My question is that I have a gas fireplace that is a bump out from the back of my first floor family room.  The floor joists under it are cantilevered in place and extend about 28 inches out past the other rim joists.  How do I insulate this space:

Option 1: 2 inch foam board along the rim joist that is now 28 inches behind the existing rim joists (backend of the cantilever) and 2 inch foam board on floor of the cantilevered section (basically is some type of metal/vinyl material) and ceiling gaps with canned foam spray as best as possible (may be tough to get it perfect with it extending 28 inches back) and then fill cavity with Rockwool.

Option 2: 2 inch foam board along the rim joist that is now 28 inches behind the existing rim joists (backend of the cantilever) and 2 inch foam board on ceiling of the cantilevered section (below plywood under the gas fireplace insert) and sealing gaps with canned foam spray (may be tough to get it perfect with it extending 28 inches back)and then fill cavity with Rockwool.  With option 2 is it ok to have the foam board against the plywood under the gas fireplace.

Option 3 – Something I’m not thinking of.

Thanks,
Mike