I haven´t shipped in or out of Mumbai, but almost everyone who has, reports it was terrible. Me, I´d probably go somewhere else to send the vehicle!
I have shipped a bike, by air, out of Chennai to Bangkok 4,5 years ago, and yeah, it was a big hassle (I remember we spent roughly about one working WEEK in Chennai just running around the city sorting out all paperwork, packing and customs clearance stuff, which was actually handled by an agent, but nevertheless kept us busy, too!)...
But for us, it was otherwise okay, no hidden costs, and generally everything went the way it was planned, it flew on the correct flight, and arrived in Bangkok without any damage. Just a lot of work, even when using an agent (and in India I wouldn´t want to try without one!) The freight agent we used in Chennai was Shell Air – I have no idea, if they even exist any more, but if you want, I can look up, if I still have their e-mail address?
Do note, that freight agents didn´t seem to return e-mails very quickly, and generally didn´t get the wheels rolling, until we showed up with the bike at their office.
And I was warned at the time not to send to Laem Chabang seaport in Thailand, because it was claimed to be corrupt. I think some people have sent vehicles there later on, so maybe it is better now, but thought I´d mention anyway.
ps. I think during the time of our trip, there was a big cargo ship with 5-6 cabins going from Singapore (maybe, or could have been Pt.Klang, Malaysia) to Chennai... for us it would have been more expensive than airfreight and our own flight tickets, but sending a car, maybe it could be an option, if it is still going. Remember, it´s not a car ferry, there are no ferries on that route. Sorry, I can´t remember more about it.