Wow, you managed to coherently use Sagan and Evangelion -- two of my most favorite things -- in one post? Brilliant!
The dimensional perspective can certainly be used to explain many aspects of the UFO phenomenon.
In particular, I wonder about the interaction/contact/communication aspect. The analogy of a human interacting with an ant (or a dolphin for that matter) is often used to explain why a non-human intelligence might not want or be able to communicate with us. However, if there is a dimensional component, that could obviously create an interaction barriers as well.
For instance, the apple may want to interact with the flat shapes, but doing so is challenging - both from the apple's perspective and the perspective of the 2D shapes. The apple must communicate 3D information and concepts in 2D form to creatures that exist, experience, and think in 2D. (What might that mean to
think in 2D; and I don't mean conceptually -- I mean their brain and mind
are 2 dimensional.)
If there are non-human intelligences that exist in more than 3 dimensions, assuming they are conscious, then one must assume their consciousness exists in more than 3 dimensions as well. Now, we don't understand completely how our own consciousness arises in our 3 dimensional existence, let alone what a 3+ dimensional
mind would be like.
Thus, regardless of whether said non-human intelligence was ultra-advanced or just more-advanced than us, there would be both significant physical and mental (phenomenal) challenges to coherent communication. Not to mention psychological and cultural challenges.
Of course we can assume that an uber-advanced, multi-dimensional, non-human intelligence would be able to easily overcome these challenges, but perhaps they can't. But they might be trying (
Machine Elves ). Or they might not be. What would they want to tell us? Hello? Could we understand anymore than that?