i am not an expert by any means. i do like cultural victories, and i like to MM my cities. i play mine very differently from yours, i've never tried it on a map with so many civs or with only 3 cities. obviously that means i'm certainly not at all qualified to judge if your game is winnable at this point. so, this is somewhat generic advice. but i do have some thoughts from looking at your save.
you do indeed have a lot of wonders. but some are hurting you way more than they're helping. your great person points are very very mixed. bombay's chance of a great artist is 19%, delhi's at 7% and madras is at 0. for a culture victory i try to get as many great artists as i can. if they come early, i settle them, but as the game gets later i just keep them around to culture bomb so that all 3 cities hit legendary as near in time as possible.
i'd run very different civics than you have atm. representation rather than US, bombay has 2 towns but that's all you have so far, so the extra hammer isn't worth much, and you don't have the money to be buying a lot with gold. i'd be in mercantilism rather than decentralization, just for the free specialist. but, you don't have drama yet, so you can't build theatres to assign artists. that's not a problem since i'd 100% use caste system rather than serfdom. your empire is small, your workers don't have much to do, and the ability to assign as many artists as you can afford to feed (without even building a theatre) is valuable both for culture points and for the artist GPPs. running rep adds to this since each specialist gets 3 beakers. and you have sistine chapel yay, so you get 2 culture for each one too.
delhi is running five priests. unless you really need those hammers, turning them into artists would really help the GA probability, switch the merchants too when you can afford to do that. the culture (and gold) from the holy city shrines is nice but you don't want to get too many great prophets. you have to spend a lot of hammers and time making missionaries to spread them around the globe to earn the gold, and if you use more than 3 cities (see below) then not all of your shrines would be in your big 3 culture grabbers anyway.
i've never tried to do it with only 3 cities, altho i know it's possible. with your map that cramped, you didn't have much choice. but the absolute key to my culture victories has been building the major religious buildings (christian cathedral, buddhist stupa, etc). you need to have 3 temples of that religion for each one you build (varies by map size). with only 3 cities, you're going to be limited to just one for each of your 6 religions, so think carefully where to place them. each is worth 50% culture, they're amazing. oops i do see that you have 2 in bombay already, so you knew about those. and you're working on missionaries to make sure all of your cities get each of your 6 religions, that's important too.
i try to use 6 cities for my culture victories, 3 that look good for culture and 3 spares. 2 of the spares can be so-so, they exist to build me temples to be able to build 2 cathedrals/etc (or 3 if on a small map that requires only 2 temples per) and to help with gold/science. i use the best of the spare cities to be my Great Artist farm. have a lot of food there and with caste you can run a ton of artists. ideally you have enough production there to build the wonders that give GA points. with enough food, after a certain point that city will so overwhelm the others in GPPs that you won't need to worry about the contamination the other cities give from wonders that you want the benefits from, but that give nonGA points (pyramids and great library for me). a prophet or 3 is useful for the shrines, if you found religions and have the time to spread them, and you ideally want 3 scientists for academies, but with micromanaging and some luck with the random rolls that's doable. sometimes that later-founded GA farm ends up catching up culture-wise with the city you'd thought would be the 3rd one to hit legendary, so that's another reason to get lots of GAs and save them, to know which cities to bomb.
what surprised me the most when trying out and learning culture victories is that the early game is crucial in terms of city placement and certain wonders, but you really don't need to watch how fast your cities are gaining culture until much later. the game totally changes once you get the key buildings built in your 3 core cities. at a certain point you even stop research (which seemed blasphemous to me!), turn up the culture slider, watch your diplomacy with the bad guys, and the tide completely turns.
this link is for a peaceful cultural victory, obviously midgame and with toku being such a pain to you a lot of it doesn't apply. but it might be helpful advice for this or next time.
Godotnut's War Academy Article
good luck!!
