Previous PE experience but unconventional background - how will this affect internships/jobs down the line?

I come from a pretty uncommon background: graduated with a 3.0 gpa at a no-name public school, majors in engineering and economics. Worked as an engineer at a very small company until recently when I was able to get my current position as an analyst at a small private equity firm. My plan is to work here until starting b-school in Fall 2015, so I'll have about 1.5 years in private equity under my belt and possibly a promotion or two. I'm going to be applying to HBS, Wharton, Columbia, Booth, Stern, Kellogg, maybe a few others. Ideally (based on little research) I'd like to go to Booth or Columbia. I think H/W are long shots but I'd like to apply for the hell of it.

I'm just wondering, with a fairly unconventional background like this I've heard even with the PE experience and good b-school it'll be tough to find internships and full time positions at better name firms. My firm is small - just myself and the partners - so I get to get involved in pretty much every single aspect of every deal and portfolio company that the partners do (for example, just two hours into my employment I was in a meeting with a management team about a management buyout, and the partners have since entrusted me with modeling the deal and updating based on how our negotiations with them have been going). My ultimate goal is to source a deal for them that they end up acquiring, but I'm only in my third week and don't even have business cards made up yet haha.

Anyways, with such an unconventional background how realistic is it for me to shoot for a summer internship while in my MBA at a larger fund or mega fund? Is it completely a pipe dream to think about applying for Blackstone's summer program?