Anyone have any clever ways to tie an invoice back to an order?

I know there's no official way to do that but I need to find a workaround so I can tell if an order was paid with an invoice that then got paid off with credit cards.

This is for our royalty report; we pay royalties on the amount of ticket sales for certain shows, but we remove a percentage from the total that we pay royalties on to account for credit card processing fees. Our latest show is almost 25% paid with the Invoice payment type because of a lot of group sales, so if the invoices are then paid with credit cards, we are losing the opportunity to reduce how much we're paying royalties on.

Anyone have any sneaky ways to figure this out?