My advice would be to take one or the other, not both. Sure it's important to have competitive scores, but the AA programs are looking for so much more than just your scores. I took the MCAT in 2005 (24R) and re-took it in 2007 (26R). As you can see my scores weren't amazing by any measure, so I struggled with the question "do I spend time and money to take the GRE to strengthen my app?" I decided against taking the GRE, applied, interviewed, and got accepted to South.
Although I definitely think it's important to have strong academic stats, it's equally important to show you know exactly why you want to be an AA and you're dedicated to medicine. Do you have any exposure other than the required hours of shadowing, like volunteering in the medical field?
Think of it this way: if you kill the GRE (which it seems like you will since you're already scoring high pre-study), then study for the MCAT (which is a beast to study for, trust me), take it, get a great score, and apply, chances are you will get an interview based on your stats. But at the interview they won't be asking you about your scores and your ambition in taking both tests. They'll want to know about the experiences that brought you to the decision to become an AA.
Hopefully that helps... good luck with whatever you choose to do!