Well I just checked a couple localities in NY (both of my parents were born there) and they do in fact provide walk-in AND mail service, for $10.00.
The third-party service offered by NY State gov is a completely different and more expensive source.
Have you checked the web site for the city/town/county in which you were born, and where your birth was officially registered?
I tried calling both the county (Westchester) and the city (Yonkers) and was told that I had to go through the state agency.
It doesn’t matter at this point. I needed it. I had to get it, so I wound up paying for it.
Mark