Looking for help with a 1960 Seamaster cal 321

I posted about this watch before. It was given to me by my wife's grand parents. It was a nonworking Omega Seamaster cal 321 CK2947 315.164. I immediately took this watch to a reputable watchmaker. No polish, except on the crystal. He has done a full service on the watch and ultrasonically cleaned everything. He is telling me that he is having problems with two parts that control the minute counter subdial. He stated that the parts are worn and need to be replaced to get this function working correctly. I realize that these parts are hard to come by. He is giving me two options. 1) To wear and enjoy the watch as is with the minute counter not functioning or 2) He has contacts all over the world and can attempt to source these original parts and replace them so that the watch works 100%.
I'm just looking for advice here because I most certainly would love this watch to work 100%. I don't have a parts list for the watch and I would actually like to search myself for these parts (on forums such as this). I know there are countless reputable people on here who would have access to these parts. I just don't know part numbers and certainly wouldn't want to buy the wrong pieces. I'm sure I will learn more today when I meet with the watchmaker but thought i would reach out here for advice. Thank you all in advance!

Here are a few pics.

Good advice. He is telling me that it may take him 6 weeks or so, which sounded more than reasonable. I will go that route. Thanks!

I'm not quite sure yet. I will find out today. He just told me that it was two parts that control the minute counter subdial. When I find out I will post again