i have a similar problem, on LA601 LAX-SCL.

AA said it is closed to even waitlist.
ON itn A was not displayed on AA/LA,
while it showed F4 on itn, (and F2 on AA7709 codeshare). It surprised me as there are only 5 total seats. that means at most one seat was booked.

i am a bit flexible on the dates, but there is a whole chain of other segments dependent. so i would like to make sure it is available before calling AA up.
is there anyway one can look at the "A" inventory on AA/LA?