Quick update:
Finally got a reply from AA Custormer service.

They totally ignored their mistakes and said that they would ask BA to be a little more helpful to AA customers who have problems.

Given 4,000 miles but no mention at all of refunding the $117 for my phone call.

Have replied and told they to re-read my letter address the real issues and come up with the money or I will sue them in small claims court.