SCOTUS has regularly intervened when a state voting case has gotten to them, usually cases around re-districting so there's precedent there.
Again, once someone sues the shit out of Cuomo and NY state itself it winds up in federal court and the appeals process pretty much guarantees that SCOTUS is going to see it.

There might be some angle that this method doesn't follow the states own Constitution and is therefore null and void.

At the least we have that angle for any congressman they try to send to DC.