I just had an illegal connection at LHR (65 minutes T4 to T1, legal is 75 minutes) but no checked baggage so the BA agent was able to force issue of both boarding passes. Took the airside bus and had 40 minutes to kill. Presume T1-T3 times are similar, but there may be special security rules for US bound flights (I believe FRA requires minimum 120 minutes connection time for US flights, due to US security requirements). I think you have to check with AA, they may arrange a car transfer for you if you have enough status or have an F ticket. Baggage can be checked, but only if you meet the minimum connection time. If you can't check the baggage through there is almost zero chance to make the connection.