If I had to give a specific suggestion on how to improve the European side of this, it would be to implement a mechanic that would allow colonizers to seize CoTs in trade company regions.
@Incompetent mentioned an expansion of the Threaten War mechanic. It's a good stand-in for a deeper system that I wouldn't mind seeing, but I think that a unique mechanic is necessary to simulate the Portuguese conquests of cities from Mombasa to Muscat to Goa to Calicut to Malacca.
I'd suggest a mechanic where the colonizer can spend DIP, MIL, and/or manpower to seize CoTs from small nations located in Trade Company regions. This is effectively what happened to Goa, for example, as well as Malacca. Give the defender the option to escalate the conflict or accept the new status quo, possibly with the addition of a truce and maybe some trade bonus.
Or you could just use the Threaten War mechanic and flavor it like "Portugal has seized one of our trade ports and wants to keep it for themselves. If we accept this claim, we get a truce with them, but if we don't, it's time for war."
Again, it's essentially how Portugal built its trade empire across the Indian Ocean, and in the absence of a way to simulate limited war, a mechanic like this could be used.
I also think trade companies should work like colonial nations in that they're self-governing once they have more than five provinces, but that's another discussion, I think.