N = 1 here, just speaking from experience from the past cycle that I just went through.
I think you could actually cut out some of the private, lower tier schools (which might not interview you given your high stats) and instead just make sure that you apply to most/all of your in-state public schools as "safeties."
In my experience (and my MCAT score was a good chunk lower than yours, with a similar GPA and ECs), I didn't get a single interview from private, lower tier schools and so the apps were just a waste of money. I'd venture to guess that you'll receive most of your interview invites from the top tier schools.