right, we are in the exactly same field then
Even if you are an affiliate business I would position yourself as a b2b tech company providing tech and other services for subscription based companies.
Put a front site up, talk tech, don;t talk marketing and leads generation, talk optimisations and BI.
Once up, go to the bank and have your pitch ready. In this situation as a solution/service provider you are looking really good.
Once the money will start to flow in, just in case prepare invoices for the received amounts (like you would be invoicing those affiliate programs, despite having self-billing signed with them)... and that's it, as legit as possible.
Everyone happy.