寿司一貫 is the correct counter!

終始一貫
shuu.shi.i-.kkan

Literally: end – begin – one – pierce

Alternately: Unchanging. Consistent. Without any variation, straight through from beginning to end, especially in one’s way of doing things.

Notes: This phrase comes to us from the Book of Han, in the chapter on Wang Mang (王莽, in Japanese Oumou).

Over the years people have invented several erroneous ways to write the ikkan part, including 一環 or 一巻. Don’t do that.

Piercing all the way through.