You should definitely check out that NY Tax team, there are a lot of experienced sellers on there.
The problem with Etsy and NY is that the sales tax in NY is based on the destination of the package, but that the zip codes in NY don't always match with the county lines. To process it correctly, you need to find out the tax jurisdiction of the destination (not the zip code) to ensure you're charging the right amount on your invoice to them.
But check out the team, there are people much more well-versed than I am and they can definitely help answer your questions about how to do this properly.
Or... if Etsy would just give us an option to set up by jurisdiction as opposed to zipcode like we've requested, we could resolve it. Good luck!!