Eehhhh
that last don’t stop us from trying.
So
Divine Hate and Divine Love are still similar - emotionally driven, ya know? Saying X represents the emotion or need Dawnshard, Odium could be X/Change and Devotion could be X/Exist
Dominion and Autonomy both have to do with control, just opposite aspects of it. This control is probably smt like Think, ya know? So think/exist or exist/think could be Autonomy, and change/think or think/change could be Dominion (change what others think)
Waddabout this:
Opposites: Same dawnshard pairs that directly oppose eachother
Near opposites: Share a Dawnshard, but have an opposite second. Example: Virtuosity, Invention: Share one Dawnshard - Change [probably]. Second would be the goal of the change - emotion vs logic, substituting Dawnshard. From this, and from something said before, it might be Need and Think, or similar themes.
As you also said, there could be an interesting relationship between inverse Shards…