Hmm...Which element of Amida cult can be importing to a fantasy war game? there are neither monsters nor powerful mages. At best you can create some zealot for Daimyo era and a priest who can reduce unrest automatically for Shinu/Jomon and MA/LA TC
. But it's not very funny IMO.
Vajrayana is much easier to present in game because it has tons of demons and sprites and rituals. Many Buddhist in old times of Japan who believe in Amida believe in it too, and it's accepted by the emperor and most mongolese officers in Yuan dynasty of China. Anyway, too many tantric elements in LA nation may be inconsonant to the theme.
I think Zen masters with astral magic and clear mind(resistance to R'yleh's dominion) may be interesting. Making them first appear in MA TC(may be heretic) but stronger in LA TC and Jomon.
About samurai armor. IIRC the Yumi(Japanese bow) is among the worst bows of the world, With the length of English long bow(many of them are even longer than 200cm), they have unbelievable short range(70 meters). So no shield is needed in ancient Japan and the banboo armor "to deflect the arrow" is very simple and only used by lower class warrior. All Daimyos and generals weared heavy armor.