Well..."ort to, ain't never" as the old family saying goes. So I accepted the job without fully realizing the extent of what I was getting into.
I started with the leather outer shell, sewing up the underarm seam first. I used double strand embroidery floss and sewed in the holes from the original seam.
Sleeves then. I actually made two stabs at a sleeve pattern. This first was really awkward:
I cut the new linings out of a hunk of black (I just couldn't put pink inside a man's coat sleeves!) and spent a couple of hours total trying to do neat, very secure, small stitches.