I'd say you've got the right idea. At the BS level, probably any mechanical/aero/astro degree is going to be closely related and acceptable to any aviation related job you may want. I graduated this May with a BS in aero, and without exception EVERY aviation related job I applied to had an aero/mechanical prereq, they're nearly identical.
As others have said, the degree is what you make of it. Sadly I'm in a similar position as you. I wanted to go military really badly but because I had $&%*&#^ seasonal allergies after age 12 I'm indefinitely disqualified, even though they haven't been an issue since I was 16.
I went to a lesser known school for engineering (ok, to be honest I went to the one with the highest girl/guy ratio I could find), and still had a plethora of opportunities when I graduated. But I busted ass in college, started a professional engineering organization, lead aviation related engineering design competitions, earned ratings, and worked an aero related internship while studying full time. It paid off though, I had job offers from more than one aviation manufacturer (including Boeing), a full ride for my MS to a major engineering school, and job offer that would pay for my MS while I worked for them full time.
The pay also beats the hell out of anything else you can do as a fresh college grad. My plan is to buy a plane straight out by the end of next summer. Then it's build the rest of my ratings, and hone in on the company/job that I can see myself staying with for a while.