Thanks! No charge for the upgrade on a F reservation. ^ I've finally figured out that in order to maximise your upgrade chances at LAX, it's good if someone in Dispatch or the back office in the Gold Desk knows your name, since they assign the cars and they don't have the incentive to charge you for upgrades.

I called in a special request to the Gold office a few weeks ago and they recognized my name -- since then, I've been getting decent or above-and-beyond upgrades on C and F reservations...