reducing your score.

There is a break point between having 9 debt accounts and 10, so if paying off the mortgage dropped you from 10 to 9, that would be a small hit.

But a bigger component is % of available credit being used. So if you have a $10,000 limit on your credit cards with a zero balance and $50,000 due on your mortgage, your credit utilization is 83%. No mortgage balance should help that ratio a lot.

Only other thought is maybe try paying off your CC's every week or two weeks instead of waiting until the due date. The card companies report your balance to the credit bureaus once a month, and your credit utilization is based on what they report. But if they get your payment 2 days after they report your balance, the balance they report doesn't change.