I can't see anywhere on members.php where they can change credit card info. There are only tabs for Main Page -- Add/renew subscription -- Your Payment History -- Edit Profile (and, yes, this is a recurring product). Going into Add/Renew Subscription gives them the choice of paying via Clickbank, which won't work for some of the products. So... 1) How do I prevent certain payment processors from showing up in members.php and 2) how do they get to change cc info in their area to enter new cc data? At the moment, I'm hoping that entering it into Authorize.Net (via 1SC) will work, doing it manually, but this can't go on.
Update cc info option will be available only if you use any cc_core based payment plugin. From your message I understood that you use 1SC and clickbank. Both these payment systems handle recurring payments itself, so user can't update cc info in aMember. Also, in regards to hide payment systems for products, you can use aMember CP -> Setup -> Advanced -> Assign payment system to a product setting.