"My watchmaker, who works at a Rolex dealer, tells me that watches of this vintage
must go for factory service. Rolex dealers can't service them, and good luck finding an independent who has parts."
Must, eh? Well this is a bit like Omega's rules for their service centers, where Cal. 321's are "Bienne only" yet I service them all the time, and buy parts for them from Omega. But of course the control Rolex exerts is always somewhat amped up compared to anyone else, but that's the Rolex way.
So contrary to you post, there are plenty of watchmakers out there who service vintage Rolex...not all of us are beholden to a brand's rules as your watchmaker is. There's nothing difficult or specific about these that makes them difficult to service, and in fact they are pretty simple movements. The only reason Rolex does this is to control the parts distribution, and to make it more difficult to get these serviced, so people will buy new instead of bothering with the old. They care less about their own heritage than even Omega does...so this is not for any "ethical" reason, and in fact I would consider it the opposite in many respects...
For the OP:
Parts for the 1210 series movements are not hard to find - I have a bunch in stock that I bought from a retiring watchmaker, because I was servicing a bunch of these at the time. Of course Murphy's law - haven't had one request to service one since I bought the parts.
😀
For me on these the bigger issue is the crown and case tube. Being manual winding watches, you need to make sure the crown and case tube are in good condition, because stripped threads may make things more difficult when it comes to service time. Case parts tend to be more difficult to get the an movement parts are, simply because they are less "universal" than the movement parts are. Rolex typically didn't use a lot of different movements at any given time, so those parts are more plentiful than specific case parts that may have only been used a a couple of models.
I've serviced a number of these, and they are great little watches, attractive, and can be made to run quite well. They have shot up in value, but were once a bit of a bargain compared to what they are now.
Cheers, Al