Is there a way to pay for subscription renewal other than with a credit card?
For example, can online payment from a checking account be made?
Also, is extension of domain name registration made directly with calssnames.net or can it be incorporated with payment to ClassCreator?

You can send us a check on a regular schedule in advance of subscription expiry rather than using a credit card. We have no means to accept checks online.

We are not a domain registrar, so we cannot incorporate that cost directly.