UPS billed $1000 in customs charges for a non-existent package

Last May, I shipped a package from Canada to a customer in the United States. I initially made a UPS Standard label, then 3 minutes later I cancelled that order and made a new upgraded Expedited label. I used the new label for the package, and tracking showed that it progressed as usual and was successfully delivered in a few days.

Four months later in October, UPS sent my customer an invoice for nearly $1000 USD. The associated tracking number is the original voided label. UPS claims a package was shipped to the United States with it and sat in a warehouse for over 40 days, incurring an $850 warehousing fee as well as associated customs fees.

There was no physical package ever attached to this label. There's no possibility I accidentally shipped a second order with it, because it was a customized product I had to special order and modify. It's been so long the tracking no longer works, but I can see in my third party shipping account that the original label is "cancelled" and the label I used is "delivered".

My customer has been trying to deal with UPS for 5 months now. He keeps getting blown off, threatened with various fines and extra fees, etc. Now the only option they're giving him is reversing the invoice charges to me, leaving me with a $1000 bill for a package that literally never existed.

What can I do at this point?