Instead of cutting a notch out, I removed the stitching at the edge of the coat to expose the entire zipper body end, and completely cut the end off. Then I stitched a complete new end on. The advantage was that it provided the maximum mechanical strength to keep the insertion pin aligned.
Careful when at the cut lines, do not pull on any threads, some are loose, but I have a way to fix that later. Then stitch using long stiches to avoid the areas too close to the cut lines where the threads are loose.
Finally, I zip the 2 halves together in order to align all the parts together into their final relative positions, and use a Bondic glue pen on all stitches and areas around the cuts where the loose threads are. When I cure with the UV light, the result is much stronger than just the threads. I was careful to not apply any of the epoxy close to the zipper, so that I don’t block the passage of the zipper slider.
Then I lightly sand to remove any sharp edges, and sew the zipper tape back to the jacket.