“ A person, firm, association or corporation having a place of business in a foreign country, state, territory or federal district and owning a motor vehicle, motorcycle or trailer used in connection with and garaged at such place of business which such owner is compelled to register in such foreign jurisdiction shall be deemed a resident of such foreign jurisdiction”

In other words, the car’s owner is only deemed a resident of a foreign jurisdiction if the car is garaged at a place of business in that foreign jurisdiction AND compelled to register in that jurisdiction. It does not matter where the car’s owner is located. If it’s not garaged in that foreign jurisdiction, it is considered to be an NY resident vehicle.

Your workaround does not work according to NY law because your car is not garaged in Wyoming or whatever.