I fly out of Medford, OR, regularly and it is a pain how they have these flights that legally connect with the AA LHR flight, but the connection is usually 40-42 minutes, which is simply not realistic for an Eagle's Nest flight.
I have only booked it once, when I could confirm a SWU into J on the LHR flight and I thought there was a good chance that if I missed the connection I would then get J on the BA flight 90 minutes later. As it turned out, my travel plans changed and I had to go a week earlier and I switched to Premium Economy on the BA flight as my initial booking.