You definitely don’t want to take it to an independent watchmaker who can’t perform Omega warranty service. If you ever need warranty service in the future and Omega can tell someone has opened the case that wasn’t an official service center, you have just voided the warranty.
Frankly, based on the numbers you posted, I wouldn’t worry. The average rate when you have worn the watch is pretty good, about +3 sec/day. I assume when you have stated “dial up” for several days in a row it is not worn. It might be that it doesn’t have a full power reserve when you stop wearing it for a few days — I.e, it wasn’t wound fully or you weren’t active enough for the auto winding mechanism to wind it fully. If it keeps good time when worn, it’s working fine.
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