OK,
It is, at the moment, working the way it ought to.

I'd like to do more - like reverse the scaling in order to get the original
sphere, and have the ellipse get rotated back to the original position (I'm
probably going to have to learn about Euler angles next...) - but this is
functional.

I got the proper axes to use, and the proper matrix transform to use in order to
re-align those axes with the cardinal ones.

Holy Byzantine odyssey.

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