Yeah, i have. Well, I am from India, and probably watched Indian Films more than any other in my life...but while making the list no Indian film came to my mind that deserved to be here. Don't get offended, i am just asking, do you watch Indian films? I mean, films that are very famous and all, internationally...like, films of Ray, Ghatak, Sathyu, Sen etc?
I've seen some Indian movies, but not enough to say I have a really informed opinion, certainly. I'm open to suggestions. From the directors you mentioned I've seen Khandahar and 4 Ray films (my favorite was The Music Room). Other than that I've seen maybe 20 others (the majority but not all Bollywood). What I see when I watch Amar Akbar Anthony (it seems typical of the genre too, but that's the one that I think does it best) is a fascinating mishmash of genuine Victorian melodrama taken out of Dickens, martial arts cinema, and early-thirties '30s Hollywood musical escapism. Also a delayed title sequence that would make Godard blush. I'm not even sure how much of its effect on me is deliberate (I would guess not, and imagine as an American viewer I'm missing a lot of what the original Hindi audience saw), but cinematic dilettante that I am I find it very appealing.