Hi Ben,
first of all: Unfortunately there ist no standard functionality to upload expense reports in mass.
But the current customer process with a single point of uploading excel files sounds to me like a organisational problem for which I would recommend to do it like in ByDesign standard scenario. That means let employee creating their expense reports in ByDesign directly, only in this case you can use standard workflows. Yes that means more licences but only Self-Service licences and for me it sounds like a more efficient way as the current. This is my opinion and the answer I give our customers if they ask.
The other standard way is the central record of expense reports in Travel and Expenses Work Center -> "Expense Report On Behalf" but I think you already know that this is a lot of work.
Your workaround with supplier invoices could work but in this case you have to definitely talk with an auditor before because for every booking you need an receipt and in this case the receipt must be an invoice from employee. You also have to pay attention to the fact that this supplier upload sheet (standard functionality) only allows, i think it was 30 line items per invoice but you could also develop an own upload function, web service for that is available.
Another solution can be to check SDK possibilities, I don`t know exactly the BO for expense reports but it coud be possible to provide a web service for it.
Best Regards,
Andreas