Okinawa

Seeing that Sucker Punch managed to tell the less known story of the Tsushima Samurai fighting against a Mongol invasion, and now the story of the historic Ainu from modern Hokkaido. They could pick another interesting contrast of modern day Japan in a third game by focusing on the Ryukyu kingdom (modern day Okinawa).

The Ryukyus were sort of their own society, close to Japan, but not quite Japanese. They had trading ties with the Chinese Quing Dynasty. Just like Tsushima, they forcefully drove off multiple Mongol invasions. Then they were invaded and subjugated by Japan via Satsuma domain in the name of the Shogunate, but kept their independent status and trade connections with China. In the late 1800s, during the Meji period, Ryukyu was formally annexed into Japan as the Okinawa Prefecture.

If Sucker Punch keeps searching for stories that are "more than just Samurai", like they seem to do so far, this could be it.

Okinawa is also the original birthplace of Karate. And Mr. Miyagi, from Karate Kid, that's a typically Okinawan surname. I think the actor even was Okinawan, but i'm not sure about that aspect.