However, it would have been funnier if you said you're a rocket scientist

.
(I have an acquaintance who
is a rocket scientist. She said that she got tired of the phrase, "It's not exactly rocket science!" really quickly.)
I've actually not gone to many instrument repair techs. I went to two based on word-of-mouth and two based on, "They're close and I need something easy/cheap done." If I didn't know of a tech in my area, I'd probably hit the National Association of Professional Band Instrument Repair Technicians
website to look for a tech close to me and then hit the
Better Business Bureau (or your local equivalent) that's close to me. While I know that neither
guarantee me a good tech, the combination does make the
probability of finding good tech much higher.
Looking over the application form at NAPBRIT, I do see multiple entries asking about schooling, apprenticeship and how many years of experience you have. FWIW, I finally finished my BS degree in IT two years ago. However, I've worked on computers professionally for 25 years. The experience and my professional certifications have always outweighed the degree in the jobs I've had.
Oh. Experience doesn't even guarantee good: several years ago, I worked with a person that was with my company for six-ish years. She had no computer-industry certs and no degree in an IT-related field. She wasn't exactly a good tech and the other techs and I tried very, very hard not to give her any tickets for even moderately complex computer problems. Why? It was much easier for one of our good techs to fix the initial problem than to fix the problems
introduced by Not Exactly a Good Tech.