-I am essentially shooting for a 760+ GMAT. I consider myself to be a good standardized test taker (176 LSAT/2380 SAT). I say that not to brag, but just to point out what I believe would be the strongest part of my application.
-Now here's my glaring weakness--my only WE consists of four positions--three of which were internships, and only one of which was paid. I know that puts me way, way behind the curve at a place like Darden. The positions I've had are good and reputable in their own right, but they aren't IB or consulting, and two are public-sector. If I matriculated in fall 2014, I would be barely 22 years old.
Your instincts are correct. If you're going to be 22 with mainly internships as your WE, it's gonna be tough sledding even with a 760+ GMAT. B-school admissions is different from Law (where LSAT and GPA can carry the day). If a 760 GMAT score is the strongest part of your application, you won't have much of a chance. A lot of applicants apply with strong GPA and GMAT, but what gets you in are demonstrated leadership and impact...it sounds like you don't have any full-time experience.
I suppose it wouldn't hurt to apply since worst case scenario if you're rejected you'll still be going to law school, but an MBA may be something to add later in your career, as most JD/MBA candidates are applying with significant work experience.