I'm not quite sure quite where to begin - as I was reading your post, Lisa was chortling over my shoulder as fond memories of dealing with Mumbai customs and our shipping agent came flooding back!
We actually shipped our bikes from Jordan (in a boat) so our experiences may have been different although I would doubt that flying in makes the wheels turn that much quicker.
Even if everything goes smoothly, your agent is efficient and your paperwork in order, I would allow at least 2-3 days after the bikes land in India to clear everything - our agent dealt with about twenty different people in order to clear our bikes.
Make sure your carnet is correct - Lisa's engine number was wrong which took time and baksheesh to sort out (we didn't have to pay - the agents expect it and so should include it in the price).
Our agent was good - if somewhat frustrating - and is very experienced at importing and clearing vehicles through customs. We didn't actually have to do anything except go to the port on the last day for the opening of the container and bike inspection. You could do it yourself and save some cash, but be prepared for probably at least a week of running around and lots of paperwork.
One other thing - Mumbai customs actually wrote in our passports that we had take the bikes out of India by the expiry date of our visas. This meant that any attempts to extend our visas (on medical grounds - possible for a price in Pune, or the police in some big cities) turned out to be impossible. I don't know if they do this when you fly into India - but no one that we know who arrived overland has had anything written in their passports. It isn't a problem, of course, if you're planning to leave in advance of your visa expiring.....
We keep a detailed diary on our website if you want to read all about our experiences or email us if you have any more questions.