I’m renovating our kitchen in Philadelphia and have framing inside the two exterior walls (double-wythe brick).  I was planning to spray foam (and hold my breath regarding freeze/thaw) but due to lead times and high cost/sf due to the small area being addressed, I’m leaning towards cut and cobbling. I realize the energy benefit to insulating one room of our house will be limited.

One wall is conventionally framed 2x4s and the other is a 2×3 plate with 2×4 studs on the flat.  I have some 3″ polyiso to use for the conventionally framed wall and was thinking I’d get 1″ sheets of foil faced polyisio to use on the 2×3 wall sliding 1 sheet behind the studs and sealing those seems with foam before adding a second layer in the stud bays. 

My questions:
1. Do I need to seal with caulking or can I rely just on the spray foam?

2,Considering the diminishing returns with a partially insulated house, is it worth my time to cut and cobble as opposed to a careful air sealing of gaps and cracks and installation of an alternative and easier to install material?

3. Is all this ill-advised or is there a better approach?

Thanks!