Thanks to everyone for their time and advice. After 75 minutes of trekking through LAX and hanging around at a rather far flung gate I now have a boarding pass. Boarding starts in an hour and the gate is quite a trek from the lounge so my lounge time on what was supposed to be a 4.5hr layover (cut to 3.5 by a schedule change) is down to about 30 minutes.
I appreciate the help from FTers but I am very unimpressed by this circus. If AS and FJ are serious about being part of a global alliance they need to learn to communicate better. I suspect the problem lies more with FJ than AS as it was their call centre which (twice) gave me completely the wrong information about having to go landside.