If I were finishing this, I would cut 60° triangles to fit on two of the opposite short sides. If you’re looking at the block laying horizontally, put one on the upper right corner, and one on the lower left. This will make the block into the shape of Tennessee, and you can put them together without set in seams. Then you could make your separator rows from the same fabric. Does that make sense?
ETA: this is essentially an elongated hexagon. Here’s a pic of a hexagon quilt done the way I’m suggesting.
https://www.sizzix.com/17467/large-hexagons-quilt