Not possible - Livia's pale white magitek armour was destroyed (and by the player too no less). Besides, I'm rather cynical of the idea of trying to dangle carrots in front of players just to get them to play certain classes/Jobs. Whatever happened to playing a class or Job that you enjoy?

And for the record, I love GLA and PLD and have absolutely zero interest in those silly mounts my Legacy chocobo and magitek armour from completing the main story is good enough for me.