Hi sid05,
As you correctly identified, your lack of full-time work experience will definitely be a barrier. However, every class (at most top business schools) does tend to have a few pure science / PhD types, so it's not impossible. The main challenge for you is showing that you "get" what an MBA is about and (this is REALLY important) having believable, meaningful reasons for why you want an MBA. If it looks like you've just gotten bored or don't know what you want to do with your life, that will be a huge strike against you.
I think your best bet is to spread your bets. If you're really set on HBS & Columbia, you may be disappointed... Spread your bets to some more top-10 or top-15 schools, and take your chances. You just have to hope the right adcom is in the right mood when he/she picks up your app!
Scott