Lemay suggested to add the ability to add/change card info regardless of current subscriptions applied to the account:
This should be possible whether they have a current subscription or rebill payment or not. This would greatly enable the single click sales option you have as well.
If you can change the card in My Account for a subscription, it should be possible to change the card for other recurring billing. Such a "card update" function on the My Account page would be more intuitive for members since it is what they see on most if not all other sites requiring a card.