There is *no* reason to do a two class a340 config. I am not saying there isn't, but it would be really silly since these planes are the newest in the fleet. They are reconfiguring the 767s on some routes, but I highly doubt the 340. Especially since you are only probably adding one more seat. I couldnt imagine then squeezing an extra row in. It's possible that the LA agent was just able to look at the inventory that they could physically book. For example if you take the YYZ-LHR-HEL AY codeshare on BA, the AY agents *shouldnt* be able to see F because they can't book F.
In any event, the F and J seats are different, and the level of service is worlds apart. I have said it before and I will say it again, second best airline in the alliance.