I think chowhound.com is a better site for this type of question. I remember someone asked this very question there and someone suggested a well-hidden place in Shinsen (not far from Shibuya station) that was recommended. But it still was around 13k yen per head.
http://chowhound.chow.com/topics/829520
What was wrong with Zanmai? You say that you enjoy take out sushi but Zanmai is no good? Hmmm.
A mid-range "independent" that comes to mind is Ichikan 市勘 in Daikanyama. I have never eaten there, however. The restaurant was featured in Lost in Translation.
I went to a small shop in Ota-ku (a friend's father-in-law owns it). It was very good and reasonable. I think you pay a lot more in Daikanyama because of the rent and neighborhood. A Zanmai can make up for the high rent by high turnover.