i really think yamato is O-Inari/Inari-Okami. Oda is just combining the woman with the fox. Inari is depicted as male, female, androgynous, sometimes animal, and is a goddess of prosperity and granting desires, so it fits with the desire to re-open Wano, bring food and prosperity back to the people and all that. Maybe Kaido wants it because O-Inari has a wish granting power?
Also, big one, Inari is also a food, just like Oden. Inari sushi.
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byakko is Monkey D. Dragon's fruit, i think