Ross, if you don't mind I'll pass along my opinion. You hit it square on the nose when you said that your major won't play an important role in your performance as an officer. Whether you were a mech engineer or a philosopher won't make much difference when the time comes to lead your men. You have to be able to adapt to the current environment and quickly learn new skills required to get the job done, regardless of your college background.
I kicked around the same questions when I was in your shoes, and here's the line of reasoning I used to make my choice.
First, pick something you enjoy studying (and can manage to pass). That makes the hours you'll spend pouring over the subject a little less painful, and your TEEs a bit less traumatic.
Second, your job as an officer (as you probably already know) will be heavily involved in planning. Fate is a fickle bitch, and there's no guarantee you'll end up doing what you want to do in life, so start using your planning skills now. If for whatever reason you end up getting out of the Army far earlier than you intended, what is your alternate plan for life? What type of job would Mr. Ross (vice LT Ross) want to do? You can use the ideas that question generates, in conjuction with finding a subject you enjoy, to pick a good major.
As it turns out, I'm glad I chose the path I did, based upon the above criteria (with more emphasis on #2).
Good luck, and try to avoid earning your STAP star.
