We simply created a phantom bank called AMEX. Where a real bank would point to a bank GL account, this phantom bank points to an account called AP-AMEX. Everything paid by AMEX is paid through this phantom bank. This records everything correctly (debits the appropriate payables account, credits AP-AMEX.) At the end of the month we pay the amount that is in the AP-AMEX account to AMEX using our "real" bank.

Works well for us.