I don’t think a shell LLC is gonna help you avoid the requirement to register a car you own as a New York resident. The law in New York requires that for the vehicle to be considered non-resident it be garaged at the out-of-state place of business. Taxes are irrelevant.

You are mistaking ownership and falsifying who owns the vehicle. Do you understand how ownership is defined, legally? How can you simultaneously own a vehicle, and the LLC too?

If the LLC owns the vehicle, you do not.