We came up with a pretty crazy workaround and I want to share it.
Instead of importing the order list into File | Import | Order List to Invoice, they now import it into File | Import | Update Orders, and the template puts an "X" in the Ship Via field.
Then they use the Order Entry | Auto Invoice Orders function, sort by customer, and filter on the Ship Via field ("X" only). We created a Favorite for this purpose.
Luckily for them they do not use the Ship Via field; the field doesn't have to be Ship Via, but it has to be one that is a) not used, b) available in the Import Update Orders function, and c) available as a filter in the Auto Invoice Orders function.
They are looking forward to a future release of OrderEntry that assigns invoice numbers to imported orders based on the list itself.
Steve