Based upon my experience, if you currently have 2 conditional appointment (pending 2 waivers), then you technically can't accept either appointments. In other words they don't send you papers to sign unless you are given a waiver.
Additionally, once given the waiver (which can happen well after MAY 1), you can still accept the appointment.
If I were in your situation, I would put a deposit on a non-service academy college or university, and do everything to show that you will be going there (cause, well, you might) -- and then when your waivers start rolling in you can choose to accept them and accept your appointment. Good luck in gettin those waivers, and congrats on getting 2 appointments.