I don't know about EC's but they do factor in work experience and professional certifications. If you could knock out the CPA exam and maybe the CMA exam that would be helpful. If you take the CPA exam first you only have to take 3/4 parts of the CMA, which is why I suggested both.
Like you said the program that you go to matters, but some of the best accounting programs aren't necessarily at Stanford or MIT, some state universities rank very well. I found an older ranking of programs when I was looking into all this, I'll try to refind it and post it. I've also been told to not go to school in the same part of the country you hope to work.
Also, don't let the GMAT stop you, if you put in some real effort into studying for it I'm sure you'd do fine. If you do the CPA first that'll give you plenty of test prep practice!
Okay found the PDF with the rankings from late 2006, if you want to see it PM me your email and I'll forward the file, not sure if I can post PDF's here.
It's from the Public Accounting Report, and ranks accounting PhD programs up through 25. Here are the highest ranked:
1. UT - Austin
2. University of Michigan
3. Stanford
4. University of Chicago
5. UIUC
6. University of Pennsylvania - Wharton
7. UNC - Chapel Hill
8. Indiana University
9. University of Washington
10. Cornell
11. University of Southern California
12. Michigan State
13. Harvard / Univ of Iowa
15. Arizona State
MIT's program actually didn't make the top 25.