If you can't get it up to a Federal court that will actually do something about it, and make no mistake, the Federal district that covers New York will very likely *NOT* do anything about it, you are just not going to get anything to happen within a sufficient time frame to prevent it from interfering with the election.
I agree with you that the Federal district courts that cover New York will not only very likely, but beyond a reasonable doubt, not do anything about it.
A system that works like this is a non-functional system.
The system you describe is non-existent.
The final decision of the State is not appealed to a district court. The U.S. District Courts are trial courts, not appellate courts.
There are many U.S. District Courts in the state of New York.
The Northern District (NDNY) courts are in Albany, Binghamton, Plattsburgh, Syracuse and Utica.
The Eastern District (EDNY) courts are in Brooklyn and Central Islip.
The Western District (WDNY) courts are in Buffalo, Rochester, Canandaigua, Elmira, and Jamestown.
The Southern District (SDNY) courts are the Thurgood Marshall United States Courthouse and the Daniel Patrick Moynihan United States Courthouse, both in Manhattan, the Charles L. Brieant Jr. Federal Building and Courthouse in White Plains, and the United States Courthouse in Poughkeepsie.
Like I said, it is a broken system.