I agree with the other lawyer. You might check with some counties upstate where the wait time may be shorter and see if you feel comfortable doing it yourself. You can also use the Avvo find a lawyer feature to look for lawyers who may be able to refile you in a county with a shorter wait-time. You should probably also talk to an immigration lawyer.
Normally in Upstate New York, a cover letter asking to expedite with a valid reason will suffice. The turn-around time is 2 to 4 weeks, depending on whether any issues are raised. In one case, the judge bypassed the magistrate review and issued a judgment, thus quickening the process. But the judge is a well respected judge.
Since you already went to the trouble and expense to file in New York, and since generally a divorce there takes about three months from filing to finish, you should have your divorce in about a month at this point without having to start over. Perhaps you could go into the Clerk's office and talk to someone and inquire as to where you stand and, with your fingers crossed, someone might help you...
The reason you stated would normally be good, except in NYC they are not expediting divorces unless the reason is extraordinary. Over the summer they refused to expedite a client's divorce even though she was due to give birth in one month to a child conceived by someone other than her husband. Sit tight and hopefully they sign it soon.
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