I'm having particular trouble coming up with a good term for "Chaotic"; most of the synonyms seem
to be negative-sounding!
Also, what would you think of rating a character or monsters adherence to a
Alignment by degree? Instead of every, say, Lawful character being described by the same one-word term, the term would be modified by another term like "Strongly", "Moderately", or "Weakly" (or some other equivalent words)? Perhaps with game-mechanical effects (i.e. characters who are "Strongly" Lawful would fare better on Mechanus and worse on Limbo than a "Moderately" Lawful character, etc.)
Are there any missing Alignments? What do you think of "Unaligned" being added to the game, as in 4E and 5E?
Synonyms for chaos are negative because chaos is typically an unwanted and adversarial state. It's one of the weaknesses I've always believed exists in the D&D alignment system; chaos is bad.
Chaos as originally so named was not about randomness but about formlessness: "tovu v'bohu," the Earth was "without form and void": it was Ginnungagap, the Abyss, the gaping maw of nothingness that was to be filled by Creation. What is not nameable or subject to law cannot be spoken of or subjected to reason: it is madness. The Far Realms are more chaotic than the eternal randomness of Limbo.
Synonyms that might not be quite so pejorative include Luck, Chance, and Fortune. Law is often paired with Order, Rigor, or Fate. Ancient terms for the grand scheme of things are Cosmos, Logos, Dharma, Tao, Rta. Thus you might have the forces of Logos arranged against those of Luck; of Form battling the Void; of the Stellar Order of the Cosmos (symbolizing the grand scheme) struggling with the Host of Meteors (one-off events that are unpredictable and inject randomness in to astrology).
As an offhand note regarding Logos, a long time ago I was trying to come up with a non-dual arrangement of moralities, instead of two versuses. I finally suggested that there could be Logos, Ethos and Pathos; three ways of conceptualizing the world, each with their own moral scales. Here's the short version from which you could build conflicts between perfectly well-intentioned entities that disagreed with each other as to means or ends:
Pathos on Ethos: "If your ethics cause sadness, they're inherently wrong."
Pathos on Logos: "If your logic doesn't make people happier, abandon it and follow your heart."
Ethos on Pathos: "Hedonism is shortsighted; ethics is historically accumulated wisdom that takes people's interests in to account."
Ethos on Logos: "Logic can lead to morally untenable outcomes, in which case it should be abandoned to go with what is right."
Logos on Pathos: "Following immediate gratification does not optimize long term outcomes."
Logos on Ethos: "Ethics that conflict with facts on the ground must be amended."