I can appreciate the anxiety given the past history, but really it's easier to deal with what actually happens rather than what might happen.

In the event there is a cancellation I would guess you'll be routed through JFK or another East Coast airport on BA and/or AA. If there is genuinely nothing available then you can ask to be put onto the United flight or some other routing getting you in the same sort of time you would otherwise have been schedule. But it's really difficult to imagine BA won't have something suitable. You'd almost certainly be able to deal with this online too.