@VIZ1 Here are some random musings fed by lack of sleep:
First of all, I'm sorry. This really sucks and I'm sympathetic to the fact that it really sucks. I've played the waitlist game and it's not remotely fun, and I honestly can't imagine what it's like to go through that for multiple applications.
First, the school issue. I'm going to speculate wildly here. When you say "mid-tier," what kinds of schools are we talking about here? For example, there are a lot of very small, specifically focused schools that I think one could describe as mid-tier. Likewise, there are also a lot of bigger schools with fairly reasonable admissions averages located in neutral parts of the country to which everyone and their cousin applies (think schools like George Washington, etc.) Normally, I think stories of "yield protection" are pretty far-fetched but in this case your scores are extraordinary and it could very well apply. If one of these schools with 10000+ applications, who can basically afford to throw out any application that has the slightest problem, sees your numbers I could see them assuming that you probably wouldn't come to the school and not wanting to send you one of their few interviews.
I recently attended a talk on residency applications. A different ballgame, but I think that the same principles apply. A program director said that due to a phenomenon called "application bloat" a lot of programs see competitive applicants applying from some completely different place in the country, assume they're doing it just to add an extra safety factor to their application, and because of that don't get an interview. But he also said that this can sometimes be avoided by an email, specifically explaining your motivations for that program beyond the application itself. Perhaps something to consider? In a lot of cases, this sort of thing might not hold a lot of weight--and it still might not--but your extremely strong numbers might give it some extra horsepower.
With regard to the interviews, six waitlists is not a terrible place to be in. They also have a reason for waitlisting you and not outright rejecting you. So you're definitely still in the ballgame. I would recommend keeping in contact with some of the admissions offices without being annoying. It's generally against SDN dogma to send unsolicited messages to admissions offices, but I disagree. I think that you want them to recognize your name and your story, so that when it comes time for them to pull from the waitlist you're at the front of their minds. All this being said, it does seem like you have an unusually large number of waitlists. If you don't get in somewhere this year (and I truly hope you're not in that position) I would strongly urge you to contact all of the admissions offices where you were waitlisted and ask them for feedback. They might be able to provide a perspective to your interview that you can't recognize yourself.
Overall, I wish you the very best of luck...I hope that things turn around soon!