Apart from creating a brand new class and leveling him via kill 10 rats leves and soloing FATEs (i have almost no quests left except for a few in the very late 40's), is there ANY - I mean ANY - method of leveling up my Chocobo somewhat faster?

Seriously, a kill 10 rats leve barely gives him XP that is remotely noticeable on its XP bar. I would prefer not to kill 5000 mobs straight, just to level him up.