Psyren is my favorite manga and D.Gray-man was also in my top 10 until it went monthly.
I'd suggest the first two especially:
Hoshi no Samidare - Doesn't have lots of action (even though it has some pretty awesome fights later on) but makes up for it with awesome characters and story. Completely amazing manga.
Id - Some of the best battles I've seen. The beginning is slow and feels lame but like 20 chapters in it starts getting faster. The story develops and becomes amazing but only later on.
The Breaker - Has very good action scenes. The story is fast and keeps up well with the action. Has a lot of hilarious comedy scenes, especially in the beginning. Very well done and not too big. It is slightly different from the examples you give and what I suggest but the essence is there.
Kekkaishi - Not a lot of awesome fights. Good characters and the story develops nicely. It's a little long but still a pleasant read.
Veritas - The story takes a secondary role. It has quite a lot of fights and some of them are pretty good. The ending sucked though and a sequel starts feeling impossible by now.