: Oh, that's too bad. I've asked Abel if he'll have me back, so to
: speak, but I'll need some luck.

: Would it be advisable to try using the official TAG Heuer service
: department (presumably via Tourneau) for repairing vintage
: Heuers?

: I wouldn't generally think so, but I came across an old post saying
: TAG Heuer service was "running low" on vintage parts,
: which I take to mean they at least know what they're doing... so
: long as they have parts in stock.

It is true that original vintage parts are running low pretty much everywhere, and at TH too - but they have definitely revamped the vintage restauration business under the leadership of Catherine Eberlé-Devaux.
They do wonderful work and there is now a very careful approach to vintage pieces. So if I were you and Abel's list were too long, I'd definitely consider TH Heritage Department at the La Chaux de Fonds HQ - also see the very nice informative story by David at Calibre11.com (https://www.calibre11.com/tag-heuer-monaco-1133b-piece-dart-and-the-heuer-heritage-department/).
Sending it to Switzerland from outside Europe could be expensive, but you'd be in safe hands.
Cheers,
Fabrizio