I know thats what i plan to do. Im going to put the Bahaminis in a Persian primary culture and give them modiferes to cancel out the wrong culture and what not. But the problem is the Sultanate of Gujarat should actually have the Gujarati prim culture. The mughals have Uzbecki, Delhians have perisan, the Bengali should have some kind of Afghan, Janpur (bihar in vanilla) was actually a muslim state not a hindu state theres not much on them but im assuming they should have Bihari or Hindustani Primary culture.
Seriously the India is EUIII is so badly done. I mean Kanauj (the culture in most of North India) is barley even spoken in India, it should be Hindustani or something. Seriously, one trip on wikipedia can improve it compelty. I mean they even put the Himalayas in India! It goes through Delhi >.>. I mean I dont want paradox to did what i did with my AO, but just a little bit of realism would do
As I've mentioned elsewhere I'm releasing a primarily indian oriented mod some time in december or january and I agree completely. "Kaunauji" culture I think is passable however as culture isn't necessarily about language and the hindi language isn't formed yet at the start of the game (the culture group is indeed called hindusthani and I made a region for northern india called Hindusthan). Kaunaj is in fact a region as well as a (much older) language and so I've considered the culture to refer to that rather than the language (but a better name would indeed be nice, though I think Hindusthani would need to swallow up atleast awadhi as well to be logical).
Perhaps the culture could be named "Upper Doabi" or somesuch? Though that doesn't sound very nice...
I've taken a somewhat similar approach on the often foreign reigning aristocracies in the muslim countries to you but would like to make a point about Gujarat and Bengal:
I think both could have indian dynasties rising to power. Gujarat _was_ ruled by converted rajputs after all, and as I mentioned a hindu vizier did take power over Bengal and then converted and named his son Mohammad and made him sultan (That's the ganesha dynasty in vanilla HTTT's files).
I would also like to make the point that by the game's start india has had a muslim aristocracy for so long that inserting some of those "foreign" families into the indian culture groups wouldn't be amiss at all. There are also several examples of hindu nobility converting and ruling muslim states, I'm not sure if the opposite happened however (the one I can think of is Mysore but that state rather became muslim when a muslim dynasty took it over in the 1700s).
Most of the hindu nations in this game did have a large element of persian/afghan/arabs in their militaries and nobility so having those elements take over wouldn't be unthinkable (according to some sources the founders of the Vijayanagar empire themselves where at one point Muslims, whether this is true or not I cannot tell but even according to themselves they did serve as officers in the muslim armies before founding their nation).
One last point

:
The mughals should not be uzbecks, there were no uzbeks in Samarkand when they left it. The uzbeks where the one's who chased Timur away from there and then settled and that's the reason the area is predominantly Uzbek today.