Get yourself a vulture and go kill ovis, but let the vulture harvest it (you can't put anything in it's inventory, it has to harvest it on its own), and the vulture will keep raw mutton fresh for 2 hours while you trap and knock out your griffin. No kibble needed, nearly max taming efficiency for the cost of a few spoiled meat to tame a vulture.
Absolutely fantastic mounts. Up their stamina a few times as well as their weight, and you've got yourself a fantastic globe-trotter. I use mine for getting supply drops at night. Put an otter on your neck for temperature regulation or a Jerboa as a backpack and you've got yourself a perfect world-traveling setup. Griffin's are absolutely fantastic 10/10.