Just flew TN business yesterday on AS miles. Use *A lounge.
I have been to AMEX lounge in the past for other things and agree it is far inferior.

Gate for TN was 208 which is a good 10-15 minutes from lounges.
Left at 9:30pm- had to get a TN BP at gate (as had an AS BP) and boarded less than 5 minutes later. Flt scheduled 1045pm.