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If you go there I would ask him how many Speedmasters he has worked on. Bear in mind that chronographs are a lot more complicated than a regular time-only watch.
He may also not be able to order genuine Omega parts if he is not accredited.
Swiss Time Services or The Watch Atelier are reputable accredited places to take an Omega, but as ejay said it will require a full service (though that will be the case regardless of where you take it) and the associated cost.
Haven't tried him yet, will bring my Turtle there one day, but he looks like he knows what he is doing:
https://www.margoliswatch.co.uk/