Need a solution for Paying only Discount Invioces in a Payment Batch

Here is the situation.  Currently we are missing out on discounts due to the fact that there are invoice due dates that are falling on the weekend.  The company does not want to use the Pay Through Date field to resolve this because it picks up all invoices through the weekend not just those that have discounts on them and this is causing a Cash Flow Issue.  They would like a way to pay Invoices that have discount terms with due dates falling on a weekend in their regular payment batches with all their other invoices that are due. Currently