You are most definitely NOT too old for an MBA. Geesh! I am 44 and currently pursuing my MBA and yes I may be a little bit "too old" but I am truly enjoying academia and I am thinking about applying for a PhD program.
So let me tell you this.
I am not at a top10 university... my university is somewhere in the middle... so nothing "special" but the program is still awesome and the tuition rates acceptable.
There are students in my class who are 23 years old because they went straight from their undergraduate to their MBA.
Many of my professors have said (and I have always had excellent relationships with professors so they really do tell me a lot) that getting your MBA this early will do almost nothing for your career. There will not be a significant boost because you haven't had a career yet.
23 year olds are still at the very bottom of the corporate ladder without much work and life experience. How can they expect that a MBA will all of a sudden get them promoted to a top executive. IMPOSSIBLE. You still need the life and work experience.
So no I think you are absolutely on the right track to gain experience and then get your MBA. You are NOT too old for an MBA. I am absolutely sure about that.
There are many 30+ year olds who get an MBA and I would even say that late 20s is the perfect time to start. Not sooner.
The only "small" problem that I see here is your GMAT score. I mean I didn't score much higher than you but like I said I also never applied to a top program. If you want to get into a program at a high level university you need to be well above 600.