At least, one comment. Thank you Rob.
You got it perfectly right. I have used a different notation, but this doesn't matter here.
F:N|C:P+O|E:N - you use the 2x2x2 but the "corners only" 3x3x3 has also been made (not to mention Oskar's Gerardo's Cube
Oskars invention would suffice too. I (and most other readers) don't own one but almost everybody ownes a 2x2x2.
F:O|C:P|E:P - for this one it is tough to see that the corner pieces are different colors - they all look gray
It is hard to see but they are not all gray. They have 4 different colors.
F:O|C:N|E:P+O - this one is an octahedron and I am curious why this goes here - it has the "base" pieces which do not appear in the others - you could apply a coloring to the "simple edges only" that would make center orientations matter.
Correct with your last point. A super simple edges only (cool name, btw) would suffice. The octhaedron is the cornerturning one. Cornerturning octahedron is equivalent to faceturning hexahedron. If you ignore the trivial tips you get a puzzle which fits F:O|C:N|E:P+O. Christophs Magic jewel has no trivial tips, means it is more appropriate. I choose this variant because I own it (compared to the magic jewel and another edgesonly cube) and it was massproduced at one point in time.
F:O|C:P|E:P+O - you use the trajber's octahedron, but this is also possible with a 3x3x3 coloration
Correct. But again I preferred the Trajbers octahedron because it wass massproduced in the past and is now again.
Lastly, should the framework be expanded to distinguish between 90/180/270 orientation possibilities on the faces? For example, to encompass the Rubenking:
Actually, the Rubenking is not a good example for where only 180 orientations of the faces matter but 90 degree rotations don't... hmmm... is it even possible?
They only massproduced example I know of is the monochrome pyramorphix. It would be cool to expand this series. But so far I don't have a single variant of those 9 additional ones.