No ARCS. How are others clearing Credit Card Invoices and Reconciling in Cash Management?

Summary:

My organization has a custom payment processing tool for Credit Cards. We capture up to 80k a day. We have regular check, cash, and other payment methods, but most are credit cards.

For invoices using check, on account, or other payment methods, we intend to create invoices and clear with lockbox receipts. However, with Credit Card, we complete the authorization and capture and are not yet sure if we will create an AR invoice for these since we could clear them with a receipt from our nightly authorization file. The cash clears later and appears in our statement from the CC companies.