Assuming I get a 650, do you think that will offset my low GPA? To me, it seems like I should be given consideration of the low GPA because of the undergraduate in Engineering and Math. I feel like if I had chosen a BA in Art History it would have been much higher...
If I were to take some courses in finance/management and built an alternate transcript with A's, do you think I would have a chance at UNC or other schools like UNC?
I was in a similar position to you - 3.09 in Mechanical Engineering. Yes, adcoms realize the rigor of the major and the quantitative nature. Unfortunately, it's the freaks of nature who were able to get a 3.5+ in Mechanical Engineering that make us look bad. An alternative transcript is typically useful for candidates without a lot of math in their background. Yes your grades are low, but any adcom should be able to see that you took more math-heavy classes your freshman year than some people do in four years of college.
If I were you, I would gun for a 680+ on the GMAT. Take it three times if you have to. This is really going to depend on how much you want to get into a school like UNC. It took me 3 tries to break a 700, but it was worth it.
In short I would recommend this as a priority list:
1) Beat the hell out of the GMAT
2) Alternative transcript
Don't sell yourself short - yes, Utah is close to where you live, but you only get to do an MBA once...let's make sure you get everything out of it that you want.