The LLC’s ownership and Montana registration are not inherently tax evasion.

The appropriate party can pay California or New York use tax arising from the vehicle’s in-state use. Whether Montana registration may legally remain or California requires a registration from you for a vehicle you do not own is a separate question. Generally, the LLC registers it. Since this vehicle has had its use tax already paid, the tax evasion argument won't apply.

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.