Thanks everyone, it's nice to have company during a stressful time. I just got off the phone with them. The payment can't be stopped because it's already being processed - once it reaches this point there is no going back.
So, what we've done is canceled the overdraft protection so the payment will be kicked back as INSF, instead of being taken from the attached CC. I will be charged for that - by both my checking account bank and probably also by the bank I made payment to. Once it's all gone through I can call and ask to have the charges forgiven.
Now I'm just nervous as I wait for it all to play out and hope that it goes as smoothly as possible. It's scary having $7k floating around like that.
Daedala, I actually do have an Orange checking account but we've never used it. You can call me a happy ING Cultist, too

I only write maybe 1 or 2 paper checks per month, so that's not an issue for me. I think maybe it's time to make the switch.
Lesson - always double check the amount you've scheduled for Bill Pay. I think after 4 years of use I became a little too comfortable and lax.