Order tracking problem using interchange 5.10 with strap

In order to try to solve a pre-existing issue with interchange order 
numbers that were skipped through order failures, a separate invoice 
number was used. The problem with this is that there id no link between 
the card processing and the order number. If we need to check on an 
order, we end up jumping through hoops to get a transaction id and then 
go to the card processor and look it up.

Also, the customers do not get their order number in the transaction 
receipt, only the invoice number, which again, we have to jump through 
hoops to translate and find their order information.

I would prefer the old method and not worry about the order numbers that 
get lost.

Any suggestions on how to fix?