How can you own something that is owned by another company?
Or said another way, do you have any sound basis to say you are on the hook to register property in New York (you linked to a New York statue) that you do not own. Or is it the LLC’s responsibility. Genuinely curious as every state is a bit different.
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.
Who's car is it?
You seem to portray high confidence in your opinions and misrepresent your statements while fundamentally misunderstanding ownership. The moment the car legally becomes owned by another entity, it ceases being yours - this applies for all intents and purposes such as the NY statutes you share that require the owners to register the car.