I find BA to be cumbersome (have to scroll through the calendar and wait for each day to load as you click on it) and I don't have EF. What I've found helpful if I want to be sure to be in J/F on a certain leg is to just check that leg using the AA site. So, if you are trying to go to Madrid, check DFW-MAD individually, and then once you've found availability then check from your home city.