Actually all prepaid debit cards (or loadable) have a bank behind the card. A lot of my FE clients have those cards (not DE) and all you need to do is have the client call the company and ask for the account and routing number associated with that debit card. I've done this with Walmart cards (Green Dot Bank) and Nexis cards (Metropolitan Bank) with success. Don't let the fact that they have a debit card discourage you from writing them on a non 5Star/SNL company.
MetaBank and NetSpend also have routing and account numbers - but be sure to confirm with the card issuer that they are "transactional" accounts. Some have the routing and account numbers for direct deposit only, but they won't work for EFT payments.