Wylie,
Method employees will be able to give you a better answer, but as to the "receive payment" screen in Method, my understanding is that by default it directly corresponds to the recieve payment window in QB. Since that window serves only as an internal bookkeeping function (unless you also pay for the Intuit payment gateway which can be accessed directly from that window in QB), it should synch no problem with Method. So if you use the recieve payment window in Method against an Invoice, then when you open that Invoice in QB it will show it marked as paid, and you will be able to see all the info you had entered in Method.
Both Method and QB by default have a section that stores CC information for a given customer, once you enter it in the "recieve payment" window. (In QB, if you go to Edit Customer from the Customer Center, there's a "Payment Info" tab that contains that info). If Method doesn't already automatically stick that info into a new "receive payments" window for the same customer, then you could certainly customize it to do so.
Even better, if you're setting up your Method customer portal so your customers can enter their CC info directly, then Method can be customized to automatically put that info into the right tables after processing the payment, doing the same thing as if you had entered the info manually yourself.
-Sam