From other posts in this thread and personal observation, the FL at times can be (nearly) SRO.
The AMEX Centurion lounges for PLAT and higher, have some tables specifically tagged RESERVERD (for CENTURION Card holders).
I could see a situation, where there was a queue of pax waiting to get into the FL, so maybe AA should consider a similar set-up for FL: designate several tables RESERVED (for EXP/OWE or CKs)?