Dmitry-
Thanks for the suggestion. That's pretty much what I am thinking too. The customer can use secure FTP or HTTPS to security transmit a file(s) to my customer's website host, and my application can periodically check for new files and bring them down for processing. We'll need to do the usual stuff to make sure orders get processed only once and perhaps allow the customer to retrieve an updated version of the file with order numbers as confirmation, but that's just details.
Thanks.