@Carl Endres @Ajohnston 

"The "Average Days to Pay Summary" report is useless, since it calculates the customer's lifetime average, regardless of what date range I set for "Paid Through.""

Go to Reports > Customers & Receivables > Average Days to Pay Summary.  Click 'Customize Report', choose the date range you want, select OK.  That should give you the average days to pay by customer over the specified time period as one line item per customer.