File a complaint with your state’s Attorney General, FINRA, the SEC, and NYDFS. Should help Coinbase along in recovering your account. Should take no more than an hour or two to file with all regulators I mentioned.
I'm surprised OP mentioned New York State Department of Financial Services (NYFDS), but this might be the local regulator if Coinbase's home state is New York.
I would still file with them, they can still escalate on your behalf since they are the regulator, or refer you to the agency you should file a complaint with.