+1 for John. But know two things. 1. He is very fair but does do things the right way. 2. He is ridiculously busy.I've worked with all the good techs in NYC (there are only a handful) your best bet is John Leadbetter: https://www.jlwoodwindrepair.com/
He works on all of my horns, is no bs. Overhauled my alto in April which I played this summer in the Michael Brecker International Saxophone Competition.
I trust John, he will be honest with you.
You can also check out Roberto's, who at times can turn things around quickly and with great quality.
Many shops in NYC are full refurb only.
You are not going to find cheap, but you will find right.