How accurate are the AA chat team? I told them my booking reference to confirm if I have lounge access for any of the legs and they advised that I will have access in Miami, Charlotte and DFW. I am usually very sceptical of the advice provided from QFF customer service so should believe the advice from AA?

Regardless, I think I might change to go Punta Cana to DFW direct (but that involves a 4.5hr drive from Las Terrenas to Punta Cana airport) or via Miami in economy with an overnight there.