Phill:
With the info you provided in mind, I would get there AT LEAST four hours ahead of flight time to get any chance at all on the $600 upgrades. Last year, security was at code Orange, and the ATN check in was a zoo! Also, the security lines after check in were a zoo. Not enough personnel or check in stations. I hope LAX has "cleaned up its act" since then, but better safe than sorry.
Hope this helps,
Richard
