About not using the code share...

I am fully mystified as to why two people at EXP level and paranoid enough about the points to double-check that during the trip, don't even bother to verify a printed/faxed/e-mailed itinerary confirmation right after booking which would have showed the use of LX rather than the codeshare (but would not have mentioned the fare basis). It would be far easier to correct that immediately than after doing half the trip. This is not to excuse AA for any gaffs on their part but people do make life difficult for themselves sometimes. It would be very difficult to show now that you had asked for an AA code share.

The fare basis is a dificult issue since you don't see that in any itinerary confirmation, nor would there be any trace of what fare you had asked to be booked in. Since you were flying on LX for some segments, didn't you get paper tickets for this trip? If so, they would have indicated the fare basis and I would have verified that as soon as I received the ticket not to mention verify AA code shares. The reason to do this as soon as possible is that those fare codes may still be available at the time and it would be very easy to ask why you had been charged what you had been charged between the lowest price available but less than the fare basis that would have given you the full points and adjust up or down while those fares were still available.

Also what fare basis were you originally quoted at and what fare basis did you buy up to when you booked. What were you eventually booked in?

Seems to me like what happened was that you were switched from the code share to LX flights instead for which you paid the $300 additional rather than for a fare buy up. This may very well have been a mistake made by the agent and so I wish you good luck in resolving the matter but think of the trouble as an expensive way to learn to be "paranoid" about everything and assume there will be errors unless verified. You should be kicking yourself as hard as you are angry about AA agents.