I can see connecting itineraries on 6th. If you are still having problems you could also try searching at BA and move the avios over to book with them. I would also suggest using specific airport codes when searching for awards (if you haven't already), rather than NYC.

At peak times like early August you may need to work harder and be a bit more flexible to find something. That could mean a different date, or a connection, or different nearby airports at either end.