40 minutes later and it’s all fixed! I had to be really careful scraping off the old adhesive as the paint was just worn out around the trim. In fact, I discovered that this car has been repainted before! They did it correctly (removing all of the trim) which is why I thought it was original, but it has clearly had a full re-spray. The paint job must have happened pre-1992 as I have all of the records from then to now, and there’s no paint work in those records. Odd.
Anyways, the old adhesive was all removed, everything cleaned up, and new 3M tape installed. The trim piece is now arrow-straight and firmly attached to the car once more. I’ll keep an eye on the other pieces to see if they deteriorate as well.