Okay so tell me if I'm crazy.
I get some 1.5" thick XPS and rip it to 1.5" wide strips... as well as some 1/2" thick plywood.
Essentially a foam and plywood furring strip.
I create a sandwich at each stud face, and use 2" thick XPS at the header.
I suppose another option would be an 1 5/8" steel stud wall in front of the existing wall, spaced off the existing framing to allow a 2x6 rough in door...
Am I over thinking this?