Most of the monks wouldn’t make sense in holy sites. There are already Sohei Naginata so Sohei Archers would be redundant. Brahmins make zero sense as a unit anywhere.
The exception would be the Shaolin Monk which would make more sense in the Shaolin Temple than Rattan Shields do.
Rattan Shields could be made a mercenary styled after the Tiger Warriors.
The Shaolin Temple could get a heavy infantry monk unit with a Monk’s Spade.
The Chinese hero could be a Prince or General, and the healer could be a Confucian Scholar.