I brought it to a watchmaker who put it back in and tightened the screw that holds it in place once before, but it's fallen out again. I think I need to go for a full service... should I go through Omega? Or is there another reputable watchmaker in Southern California that can work in vintage Speedys? Recommendations appreciated.
Absolutely not Omega. A great recommendation for you is Al Archer. www.archerwatches.ca Strong references for Al here on this Forum. And a quick search for his posts will highlight for you both the depth of his knowledge, and the number of Speedies (including calibre Ω321's) that he's serviced.