It does seem most logical to start from the idea that the four groupings are the same as the Dawnshards, even if you don't think the actual "super-groups" are the Shards themselves. I.e. even in OP's theory, Adonalsium is broken into four aspects, theyre too big, so each aspect is broken into four more. But each of those original four Vessels was intended to wield one of the Dawnshards, and therefore relatively aligned to it.
I think the best evidence for this is trying to apply it to what we know. We know two Dawnshards: Change & Exist. We can definitely find certain shards that clearly correlate with these.
Change: Cultivation, Ruin, Invention all fit really well.
I could probably see Ambition as the 4th here (changing one's position) or Endowment (changing others through gift?)
Exist: 3 fit super well. Preservation is super obvious. Mercy (as VERY similar to Hoid's "thou shalt not harm"). Honor ("i.e. do not break your agreements and oaths").
If I had to fit a 4th here, I could see this being Devotion - again, the idea of long term commitment to shelter and protection.
Interestingly, the Change and Exist shards also seem to fit into a clear opposition with one another. That could be the same for the remaining two, though it might not be (we know something is different about one of the 4 shards, though we also don't know what - it might not have to do with that shards Command).
If the above is broadly correct, that leaves us with 7 shards with no clear home (plus one of the maybe's from above).
Dominion, Autonomy, Reason, Odium, Whimsy, Virtuosity, Valor
I personally don't take much from looking at this batch. I do feel like there's kind of a "self/virtues" theme and a "relationship to others" theme, not totally different from the "relational/personality" categories, but I'm putting very different things in there compared to OP. That might look like:
Virtues/Personality: Reason, Whimsy, Valor, Virtuosity
Relations: Dominion, Odium, Autonomy, Endowment/Ambition (whichever isn't above - Ambition fits more with them all seeming kinda villianous, while Endowment is nice for switching things up)