The most straightforward options appear to be removing the overlay completely and either painting the plated metal underneath or just polishing it out to complement the rest of the regular chromed trim. For my past FWB that I got when it was only 5 years old, I had luck with just gluing each place as it would just start to separate - usually the mitered corners and other areas getting snagged on things. On my current FWB I've had just 3 years it's getting to be a losing battle trying to keep all the covering on.
I recently changed out a rear door after an accident, and the donor's trim was so ratty I disassembled both doors and used everything from my "less than perfect" original. In the process the entire covering became disconnected on the wide vertical piece between the fixed glass and window (yours still looks pretty good in your last pic).
So, a more industrious option is finding a better JY door and swapping out everything onto your shell, which from experience will take 7 hours your first time (even with an FSM), -- and probably only 3 hours the second time, -- and even less each time after. lol
Last option is poking around for a stout weatherstrip tape and just replace everywhere, which is what I'm leaning toward. You may want to search all the threads on guys who've murdered out the chrome on their SS window trim using everything from electrical tape to special automotive material.