Thanks for reaching out and apologies for the slight delay as we were trying to hit some big deadlines with clients.
Look, I will be pretty direct here. You posted this all over the forums, so I am sure you have already been told to look outside the top 10, to share more info (this is just not much to work with here), etc.
The biggest things for someone in your situation (which is to say, very much a marginal candidate at top schools) are:
1. Strongly consider taking the GMAT again. A 660 is basically the bottom of the range where they have to read your file and not skim over it. You may even be under that barrier at some schools. It's just so hard for a program to admit someone so far below the average score and the lower you are, the greater the risk is that they won't even give you a fair review. Further, your verbal score paints you into a corner. If you struggle with the execution of your essays - as the score would indicate you might - it will tell the school that your verbal dexterity is not where it needs to be to handle the full experience of a top 10 program (course work, interviewing, and social life, all slamming you at once). If your essays are amazing, they will assume you did not write them. So you are damned if you do, damned if you don't, because your verbal score is so low. If you can increase your verbal and you can get the overall up, even 20 more points, you can greatly reduce these risks.
2. Immediately stop worrying about trying to fit in. You have to go into this being as imaginative, personable, honest, and deep as you can. If you try to walk the walk of an elite MBA, you will sound like literally thousands of other applicants, most of whom have better scores. You have no doubt heard that you are in a crowded demo (Indian male engineer), but most people focus on the wrong things about that demo: that they all have big GMAT scores, experience outside of India is the key, going to an ITT is a must, etc. Sure, all those play a role. It helps to have a high GMAT because so many Indian/Male/Engineer candidates do and you want to "keep up with the Jonses." Experience outside of India does make a big difference (or so it seems). ITT is great. However, the easiest way to stand out in this demo is to be different. Sounds obvious, right? Well, try reading 20 career goals essays or 20 "what matters most to you" essays that sound exactly the same and you will see that very few people are successfully making an effort to be different. Then try reading 500 of them. It is not just your demo that does this (churns out virtually the same exact material), of course, but it is most prevalent among Indian applicants. Perhaps this is because of the intense message board culture, where everyone is trying to figure out the "right" answer, or perhaps there are other reasons. But what I know is that our Indian applicants who have done the best are the ones that toss out literally everything they think they know and start fresh. Then, they get deep, personal, and authentic and tell a story about who they really are. My most successful Indian applicant (meaning he got into a ton of schools that he never dreamed he could) started out wanting to write about his NGO work, leading a consulting team at a big-name company in the U.S., his work ethic, and all the other things that he assumed b-schools wanted to hear. By the time we were done, he had written about his nephew, how gambling almost ruined his life, his recent attempts to become a pilot, and the night he tried stand-up comedy at the University of Texas (while there to pursue a masters in engineering). Now, I am not saying to write about those things exactly. Obviously. The whole point of this long soapbox speech I am making is to make sure you AVOID trying to find predetermined boxes to fit into. But the spirit of what he did - tapping into the things that made him uniquely him - is why he exceeded expectations.
Hope this helps you and anyone else who stumbles across the post.