I started writing this a couple of hours ago then had to leave. Forgive me if I repeat what others have said already.
Twelve Kingdoms was at the top of my list, too. You must promise me, though, that you'll watch at least until a certain rather unusual character arrives. It's about half-a-dozen episodes into the story. Youko's story ends at episode thirty-nine; there are six more episodes about another character that tell a very abbreviated story because the novelist,
Ono Fuyumi, took ill. Yes, it's the same Ono that wrote
Ghost Hunt and
Shiki.
I think you might also like
Saiunkoku Monogatari, though the protagonist is a very independently-minded female. It has a variety of strong guys in supporting roles (it is a reverse harem of sorts) and some pretty impressive female supporting characters as well. Though it has some supernatural aspects, they're much less pronounced than in either
Moribito or
Twelve Kingdoms.
You also don't seem to have
Kemono no Sou-ja Erin on your list despite your love for Uehashi's
Moribito. It shares many of the same themes as
Moribito, particularly the role of founding myths in later political events. I can't point to the fansubs any more, but they're from a well-known "immobile" group and have considerably better translations than Crunchyroll's.
There are a few shows that seemed strangely lacking from your list, making me think you'd tried them and decided against them. I'd put
Monster at the top of that list. It has a great male lead and male antagonist and certainly has a lot of focus on psychology. It's not really like any of your favorite genres, though.
Another show you might enjoy is
Welcome to the NHK!. It has elements of comedy and slice-of-life, but there's a lot of psychological drama as well. Two other slice-of-life shows I can recommend are
Bartender and
Hataraki Man. Fansubs for the latter can be found via Google.
My next suggestion actually comes in two parts. The first is the final "
Bakeneko" arc of
Ayakashi Samurai Horror Tales; the second is its unlicensed sequel
Mononoke. I've admired these shows by Nakamura Kenji more than his
Trapeze or
[C].
Finally, I'll toss out two worthwhile "B+" shows that aren't on your list.
Shion no Ou tells the story of a girl who witnesses her parents' bloody murder at age four and becomes a mute after the fact. The story follows her at age thirteen when she's trying to become a competitive professional Shougi ("Japanese chess") player. The other show is
Nijuu Mensou no Musume about a young heiress who is kidnapped by a mysterious master thief. Both of these were subbed by the excellent Live-eviL when they were doing the occasional recent series.
I don't know that any of these will knock your socks off like
Moribito or
Dennou Coil, but they're all worth watching.