It definitely isn’t ideal, but I’d just monitor the situation as the day progresses. If there is any sort of delay that gets posted, I’d get on the phone or work with an agent at the airport to re-route. Since you mentioned you can go through London, there should be at least a few seats on the other BA/AA frequencies, or re-route to not touch JFK.

Even if the inbound is delayed, but your flight isn’t delayed (putting aside padding), I’d work with the EP desk or an agent to proactively move you. They don’t have as much flexibility without a posted delay, but common sense typically prevails.