The rules for AA definitely used to specify itinerary, however I just Ctrl+f'd the detailed terms and conditions and I can't find that reference now (in practice airport didn't matter anyways as long as it was same day).

For AS, it should be the same, based on them deferring to the OneWorld terms (which are more lenient), however in practice you may have issues. I've definitely had to prove access before.
However if they have their own terms that I can't find, they may reflect more strict rules that specify itinerary. Get a paper JAL boarding pass and definitely give it a shot (and please report back with your experience since the rules aren't clear)