I think that was what you were saying anyway?

Makes sense. We don't know where Hawkwing got Justice from. If it was Amalasan's, that makes a certain amount of sense, especially if after the Red sisters with Hawkwing shielded him they let him ceremonially surrender by giving his sword to Hawkwing. I'm not sure they really had time to do that though, as the end of the battle sounds like a very confused situation.

So where did Amalasan get it from? He could have found it somewhere along the way, or (to go into real bonkers, unsubstantiated territory) maybe he was set up as a false Dragon by the Red or Black Ajah in the first place and they gave it to him out of the White Tower's stores, where it had been since the AoL?

Interesting line of enquiry, anyway.