I'd suggest that your alignment descriptions are fairly accurate for a non-D&D game. That is a game using D&D rules but not using the D&D paradigms. In D&D Good and Evil are very much universal concepts. There are two separate groups of Evil creatures killing each other endless over the concept itself, and made of Evil as physical manifestations.

In D&D Good is Good and Evil is Evil. There is no social structure implied in them. Even if all sapient life died off Good and Evil would still exist as universal constants. Baator and the Abyss are literally made of Evil in the same way that Mount Celestia and Bytopia are made of Good.

Still, a fine analysis that allows a wide range of options, even for alignment restrictions. Bob the Paladin can be kind and charitable, and Chuck the Paladin can be unpleasant and stern. Both are still lawful good, but with radically different ways of displaying that alignment combination.