OP stated that he is flying in F, so I'm not sure why the entire CW pre-flight issue matters one whit in the context of this thread.

There most certainly is a Concorde Dining Room at IAD for BA F which receives rave reviews, although it may not be the JFK CCR.

My advice would be to find the better connection.

I certainly hope that you aren't flying F to DEL and worrying about the 5A bus out to IAD !