Your credentials are stellar - incredibly strong academic profile and very strong track record within the legal field. That said, there are two major risks in your profile, which you've already pointed out: 1) practicing lawyers are a rarity in business schools (but they do exist!) and 2) you may come across as a bit of a 'robot' in your application -- need to bring out some personality and multi-dimensionality. Show your human side! Ideally you would do this through ECs and community service, but if you don't have any, you don't have any! So, you'll have to draw upon your personal experiences, interests, passions to demonstrate who you are. If you can do that successfully, you may have a chance at the programs you're targeting.
I'd also suggest that you look at University of Chicago, Columbia and NYU.
Best of luck,
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