Hi John,
If your Customer Card shows a figure in the Balance ($) field due to the unapplied CC payment, what you could do is go to a Sales Journal and enter a Refund. Then apply that refund against the payment. That should zero out the Balance($)/LCY field on the Customer Card. Things should look good from a Balance LCY perspective.
If you are strictly talking about the Payments ($) part, the Payment($) flow field on the Customer List & Stats drills back to Detailed Ledger Entries, not Customer Ledger Entries like most of the other fields (i.e. Balance ($)). When you drill back, you are unable to see any 'Application' detailed ledger entries associated with the payment to offset the balance to 0.00, so it just shows the payment's 'Initial Entry' amount in the Cust. List.
There are actual Application detailed ledger entries for the payment, problem seems to be that since this payment shares the same document # as the invoice it is not able to display properly to zero out the amount. It looks like a calculation issue with the field that Dev needs to investigate...just my initial assumption. If your new partner submits the case, references this post, then I can have Dev look into the issue. Thanks.