Breitling Jupiter Pilot Chronograph Rapair

Many moons ago, I got a Breitling Jupiter Pilot Chronograph when I earned my pilot license.
I recently brought the watch to my local Breitling shop, who, after a week, told me that the parts to repair the watch were not available anymore.

My heart sank because one, I really expected much, much more from a brand like Breitling, and two, this watch has way more than a financial value.

Breitling offered a discount on a new watch; I found that, honestly, flat-out disrespectful.

How could I buy another watch when I have no guarantee that replacement parts will be available down the road?

I'm living in Austin, TX, and wondering if anyone here has a suggestion for a watch repair shop that would take on the job and is absolutely trustworthy.