Tesla has direct access to DMV records through the state computers, just like any car dealer. They can issue temporary registration with that system.
They should be able to log on and verify current ownership.
I struggle to understand how they would accept a Bill of Sale to transfer ownership. They need evidence of completed title transfer, verified through the State DMV.
You should be able to make them look you up on the spot in the State DMV system, and verify that there is no pending transfer, and fix it.