Following the tradition that the Asian semi-civs should better be a kind of religion, I would like to introduce the Theravada Temple.
It can reasonable replace the Zen in the South and Southeast Asia. The Theravada Buddhism began to establish itself in Sri Lanka from the 3rd century BCE onwards. From Sri Lanka, the Theravāda tradition subsequently spread to the rest of Southeast Asia. Besides, the Zen Temple should not get out of Japan.
The unit of Theravada Temple can be the Flail Elephants which were said to have been a cavalry and siege unit fielded with the early armies of Sri Lanka. Just remove them from the Indians and adjust them to put them into the TP. The Indians could get Mysorean Rocket as the second castle units.
On the other hand, Lascarins can be introduced as mercenaries. Their situation is similar to the Zouave, who were natives recruited by the Europeans and serving as the colonial soldiers.
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My suggestion for the Asian semi-civs.