They will always let you pay a higher down payment. Experiences from when we had our APs make sure to pay attention to black out dates (there are a lot!).
When trying to do a lot at multiple parks the only real option in my opinion is Epcot and HS because of their size and distance from each other but their capacity really hurts (Soarin, Test Track, Toy Story), but if you want to see the nighttime shows that could change too.