Utility to clear $0 invoices off all AR customer accounts...affecting data in alerts & reporting

We have numerous $0 invoices in each customer AR account for items like samples, literature, etc. This is our way of tracking these materials. Recently, we began using bolt on programs for alerts and reporting. One report will send an alert for each customer that is past due and/or over their credit limit. The report includes all open invoices (which we want).... that means it also includes all $0 invoices since there are no payments applied against them. Is there a shortcut/procedure/utility that will show $0 invoices as paid, so they will not appear on these custom alerts & reports. We've tried using certain criteria to exclude them from the alerts/reports, but was unsuccessful.

Any suggestions would be helpful. Thank you.