If I may suggest... you could create CNs for Indian subcontinent but with triggered modifiers to make it impossible to create "settler colonies" through colonial conversion. In this way, you can have a trade company actually governing the region but doesn't displace the culture within its jurisdiction. It also means you will see trade company actually having army.

I might also say make religion conversion difficult to do but since religious unity is a big deal in this game... maybe also couple it with triggered modifiers to reduce penalty from low religious unity and to block events that might arise out of low RU.

And modify CN events from vanilla where it does not make sense for trade companies and create new chain of events for CNs with the given triggered modifiers that distinguishes it as a trade company as I mentioned above.

New possibilities here.