Well taking your advice we arrived at 5.00 am for our 7.20am departure to LHR. We actually tried to check in the evening before (when we dropped off the rental car) but hey insist they cannot check you in other than the day of departure. The agent advised getting there by 5 or 5.30 at the latest as the queue would be long.

Anyway we arrived at 5.00am. Queue were very long for check in (beyond the snakey-roped bit) and a little shorter for bag drop. I put my wife in the check in line while I went to try the FastPass kiosk. Although the first passport didn't work (scan couldn't read) the second one worked fine, and out popped out 3 BPs (including for the connecting AA flights) after having selected our seats (almost every seat was available).

Went to bag drop line and it moved quickly - approx 10-15 mins. No questions about checked luggage fees - easily tagged all the way to LAX.

Walked up the stairs from Area 14 to the security lines - not long at all - through in 10 mins or so. So we were landside by 5.30am. We walked along and saw the other security lines had much longer queues - so advisable to use the stairs from Area 14 to security lines.