AHC: Wank the Otomo Clan

So, the challenge is:

With a POD not before 1540 make Otomo Clan ( https://en.wikipedia.org/wiki/Ōtomo_clan ) the lords or overlords of Kyushu from the end of the OTL Sengoku Period at least until the XIX century.

They must be roman catholic christians.

Bonus Points:

If the south of Japan is christian and the north is shintoist or buddist.

If the leader of the Otomo becomes Shogun.

If Otomo are direct overlords of Ryuku and Taiwan, or some territory of China/Korea/Manchuria, before the XIX century.
 
The Otomo almost ruled the entire Kyushu, but the Shimazu scored some lucky and devastating victories against them.

Religion is the biggest problem here. Many local daimyo feared and loathed the Otomo for that reason alone.
 
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