I want to be careful to distinguish my personal affirmation of geocentrism as the correct view of the cosmos, from the message of "The Principle".
"The Principle" is simply, so far as I can tell, the very first full-length documentary treatment of the history, development, scientific and theological impact of, and present-day observational challenges to, the Copernican Principle.
It surprises me a great deal that no one had ever undertaken this before, but then again, there are certain things we just assume are so obvious, that we cease to even look at them.
For Newton, this was absolute space.
For us, it is the Copernican Principle.
There are many viewpoints in the film which are non-Copernican, and also non-geocentric; Ron Hatch for one, John Hartnett for another.
There is a firmly atheist Copernican in the film who concludes that the Earth is incredibly special; in fact the only place in the entire universe with intelligent life- but he arrives at this conclusion via rigorous adherence to the Copernican Principle, in its logical conclusion to a multiverse (Max Tegmark).
In short, the actual content of the film is not nearly as controversial, or threatening to any particular coalition of thinkers, as your concerns above might indicate.
Simply put, "The Principle" is not a film designed to convince anyone that geocentrism is necessarily shown to be true based on existing observations.
It is, however, quite clear about establishing that no experiment has ever shown the Earth to be in motion, and Relativity is brought into the world, in part, as a means of explaining that fact.
Geocentrism is treated both in its historical aspects (indispensible, after all, to the treatment of our subject) and in its modern re-appearance, as an hypothesis which demands considerably more respect than it will be given until it takes off its gloves and bloodies a few noses. Which it has, and will.
I regret not having had the chance to discuss this with you in the conference, but please feel free to contact me at any point along the way should you find the film, or geocentrism, to raise a question or observation in your mind.