When I sold my last home, it was in winter. The out of town buyers were not attending the closing. Their final payment was arriving by certified check via FedEx.
Except there has been snowstorms disrupting airport operations, and the check did not arrive in time. We went through with the closing anyway, signed the papers, but did not send them out until the following day, when the check arrived.
Unfortunately, you do not have that option here. The car is gone, you have signed a power of attorney to allow VW to act as your agent in completing the title transfer, and you are out on the street with a promise.
If making the decision for myself, I would probably accept that risk. But if I were advising a client, I would tell him to not leave their car without a check, even if that means rescheduling.