Except for removing the Light Cavalry tag from the [Siege Elephant], how about removing the Anti-Artillery role from them as well and give that to another unit instead?
I know that I am not the only who has suggested this, but I created a post where I suggested that the Indian civilisation could train a new unit that would be called the [Mysore Rocketeer]. They could function as a hybrid between a [Falconet] and a [Culverin] just like the [Light Cannon] for the Haudenosaunee, while the Anti-Artillery multiplier for the [Siege Elephant] can be replaced with an Infantry multiplier.
The Mysorean rocket was an Indian military weapon which was effectively used against the British East India Company during the 1780s and 1790s.
Here is a link to the post that I created for anyone who is interested:
(1 new trainable unit for the Aztecs, Haudenosaunee, Incas and the Indians)