You can mail your New York return. Just attach an explanation as to why you are mailing it. The only work-around I can come up with is to leave the state tax withholding for New York blank on the W-2 entry. Instead, enter the amount of New York tax withheld as an estimated tax payment. It's not ideal and it could create issues with New York, but it would allow you to e-file your federal return and other state return(s).
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