Looking at your MDApps, you have a very strong application. If I were you, I would apply through the regular process and see what happens. You may be pleasantly surprised. I think the general sentiment is that if you can get in through EDP, you would have gotten in anyways through the regular process. EDP is not like early decision for undergrad where there is sometimes a huge advantage compared to the rest of the pool.
If you apply early and submit everything in on time, you can also start hearing back from non-rolling schools by October 15th. That is just two weeks after the EDP people find out I believe.