LORs aren't mandatory with the primary app, so you can wait a little longer on those.
Technically, there's no point in submitting an app without an MCAT because schools won't look at your app anyway without it. Instead, to save time, submit your app to a throwaway to get it verified. Then, you can immediately submit to your actual schools of interest once your MCAT score is available.
Even if you submit to one program and not the others, it will automatically lock your app and I would only be able to add new info correct?