After evaluation by the service center in TX, if they need to send it abroad to Switzerland, you're probably looking at an additional shipping fee of $150. They may tell you in advance that the repair is going to be a minimum of $XXX or $X,XXX dollars if you send it out. Pretty much every Richemont estimate I've seen from Switzerland has been more than $1,000. Expect them to want to do quite a bit of work, especially since your watch sounds vintage. That could mean new hands, dial refinish, case re-working, etc. Turn-around time will be a minimum 3-6 months.
The concern with going to an independent watch repair shop will be if they have access to genuine Minerva/Mont-Blanc parts, and also their ability to source Valjoux 88 parts. I believe MB is like IWC in that parts are restricted to only the service center, at least here in the US. If parts need to be replaced, you may have to opt for generic versions. The Valjoux 88 has been out of production for 40+ years and some 17 variants exist for this movement - any repair will require a lot of patience!