...I got a little over-excited changing straps and turned my screw a little too hard and broke it (I forgot it was not steel - rose gold, and for a UN Maxi Marine Chronometer as well). I had to send it to UN and they sorted it out. Price-wise, it was not too expensive because I had a good relationship with the AD back then, and he managed to keep it at a reasonable price for me. I am in the same boat as you now - in a place that is difficult to get the proper rep for the watches that I have, and having a real tough time to get someone to look at a couple of the timepieces that I have an issue with. Not keen to send it all the way back to Switzerland, which I would have to do via the agent in another state from where I live.
Nonetheless, I think it's best is to send it back to UN to get it sorted, and then just be a little mindful of the screws once back from then. I guess it might be a long wait with Covid-19 delaying a lot of freight between countries (from my experience so far, still waiting for my laptop purchased more than a month ago).
All the best to you in resolving your situation.