I've never seen a TPO or EPDM gutter line job last more than a few years. They may be out there and I'm not getting called, but I've seen lots of messes.A spray coating would be the last thing I use in a built in gutter.
TPO will work fine, I'd pull off way more then the first course of shingles though, I'd run the TPO at least 1 foot up. Water stop under and felt over to the bottom, run it though the gutter and up over the edge finish it off with a nice coping metal. Term bar would look like junk if you ask me.
Ideally wrap it in S/A Base sheet and cover in copper, solder the joints. Then step back and enjoy all the compliments on your work and not worry about it for 50 years.