Well, with an annual pass, you don't pay for parking on site, even if staying off site. So upgrade your tickets at Downtown Disney before coming on site, then show them your pass when you get to the gate. They will wave you through.
All the
AAA parking pass does is allow you to park in designated "AAA" spots. I like them for EPCOT, but they aren't that great for TTC (you have to walk to the underpass and walk all the way up...I think the tram is better). At MGM it's not bad but I don't like the AK location (also well over to the side and a bit of a hike on foot).