Another excellent analysis, Rose! I agree with your assessment entirely. I especially like your distinction: Nemesis and Antagonist, the latter being a 'lesser' nemesis.
I suppose one could make an argument that since Veronica/Eden has as a key part of the Final Struggle, a battle vs. Elizabeth that Elizabeth is the Nemesis, while Him is a Trickster. But since he's the mastermind behind everything and - as you note - has been a threat to Eden throughout, I think your original instincts are right. And, as I say, interesting to ascribe an Antagonist role to Elizabeth (as well as some of the other secondary characters).
Isn't it fascinating to look at characters through the lens of these five character archetypes? It's also a great reminder of the screenwriting principle, at least one I teach and preach: Character = Function. Not to reduce the character merely to function, but rather understand why they exist and use that as the foundation for developing the character.
Thanks again!