Hi David!
I have looked at your video many times now (still no glitches as per your video capture example).
But I have spent the last several run throughs carefully examining how the elements move. To my eye all the elements look 2D-2.5D as presented.
Was there a reason why You went the video route... such as it already existed and You were expected to use it?
There have been several posts in the past on this Forum showing 2.5D effects - just using Hype's native capabilities - that would appear to "fill the bill" for the type of animation shown in your original post.
Here are two that I archived:
Hype file: Space-3d effect 2.hype.zip (23.1 KB)
A different effect:
The "original" is a cube rotation in a Scene. I adapted this original file above to a Scene transition - as the OP requested (v2 in the thread). The "Live Demo" below is now v4. They all run on a Swipe action.
Hype file: cube_transition_v4-swipe.hype.zip (203.9 KB)
In any event these are examples that might serve You well in future projects.