I appreciate the original jazz III for being one of my first steps into small pointy picks, but I definitely moved away due to QC issues and changes.
I remember emailing Dunlop and giving them feedback on a pack of the black jazz IIIs that were pretty badly made (early 2000s). It looks like they were manufactured with two sides that are then joined together (imagine an Oreo without the cream), and the joint was offset enough that the edges were catching horribly on the strings. Being nylon, they would take forever to wear in, which made them kinda useless. A rep for Dunlop apologized, asked for my address, and sent me like 30+ picks (maybe more, like a DVD sized package). All the ones that were sent not only seemed to be pretty much even with regards to the two sides of the Oreo, but the tips seemed to be smoothed over, as if a heat source was applied (the normally matte material seemed glossy). I recall them not even being in their usual retail packaging.
I eventually just jumped ship to their tortex line of jazz IIIs since they wear much better and overall have a tone I like more, but that package I was sent had the best “original” jazz IIIs I’ve played.
My long story was a setup for an answer to your question: I wouldn’t be surprised if Dunlop had a set of “nicer” production picks available at the time specifically for people like JP, and maybe still do. Maybe that additional attention to detail is what led to their line of signature picks.
Apologies if this was a non-answer, just bringing up the possibility that it’s not a consumer-available pick. Hell, maybe it’s just a small batch of picks from multiple eras / models that he’s taken the time (pun somewhat intended) to wear in just the way he likes.