I kind of see these as two sepaate decisions. What I mean is that if you're truly unhappy with your current company, then don't stay, period. That's separate from "What should I do now to help get me into a top MBA program?" My personal opinion is that, even if ths company offers you more money, bumps up your vacation, etc., you'll still be unhappy six months from now. So, you should probably go. The person who's saying "Tell us how to change, and we'll change!" is probably sincere, but he/she can probably only do so much. A year from now, I bet very little will change. It all starts and ends with the company's leadership.
Having said that, the Boeing progam does sound like it could help you more in terms of getting into b-school. Don't focus on the name as much (that matters less than many people think), and focus more on your job, what experiences you will gain, what opportunities for advancement you will have, etc. As long as you think you have the patience to stick with it for three years, it could be a good experience for you, and could help you a lot in terms of getting into school.
As an aside, you may want to ask Boeing if they have any programs to sponsor people for their MBAs. Just a thought.
Scott
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Co-Author, Your MBA Game Plan