Hi there,
Thanks for posting; sorry to hear about your dings and GMAT challenges to date.
I think your new R2 school list is more reasonable; you may have the best shot at UNC Kenan-Flagler, followed perhaps by Tepper. You may want to look at a few others outside the top 20 or so just for 'safety' options, fyi.
I agree with the other poster above about the importance of standing out in your essays; Dig deep and brainstorm on what makes YOU unique... b-school admissions decisions are made holistically... it's not just based on grades or facts or stats, but on a holistic picture of the applicant and what they'll contribute to the program, who they are as a person. That is primarily evidenced through your ESSAYS, fyi!! (And interview if you get to that point.) Elements you need to convey in your application for a chance at a top rated program include:
-what past experiences and skills will benefit you in the classroom, and later in your career
-what key traits and experiences make you UNIQUE; basically, 'why YOU??' vs other applicants
-why you want the MBA, with clear short term and long term post-MBA goals
-why NOW
-why that specific school is right for you
If you lack any of the above components, you risk that another well or similarly-qualified applicant who includes all of those, will wind up getting accepted over you!
I don't agree with the above poster that the "GMAT doesn't matter much"; the GMAT is an indicator of your potential academic performance at b-school and scoring much lower than the average can be a challenge that is tough to overcome. So I'd say a solid GMAT is necessary, but not sufficient, to get into b-school. Anyway give it your last shot and aim for schools where you scored closer to their average. Good luck and keep us posted!