How do I process a second Cash Sale (for the same items) from a Sales Order?

I have a scenario where we charged a customer's credit card for 3 out of 4 items that were fulfilled and shipped.  My customer contacted me and he mistakenly provided his personal credit card information instead of his company credit card information.  He wanted his personal credit card refunded and the amount charged to his company card.

I processed a refund against the original cash sale.  The fulfillment has not changed since the package was already picked up by UPS.  I need to create another Case Sale using the correct credit card but how do I create it from the Sales Order if the 3 items are already marked "Invoiced"?  I don't want to create another Cash Sale (from scratch and not related to the Sales order) since this will reduce my inventory again.