I'm not positive this is what you want, but there's an old thread on here that saved my bacon when I was recently trying to UV a bunch of poly strips.
1) In the UV Texture Editor, Polygons > Unitize will make all selected UV faces fit the UV space. So a bunch of squares stacked on top of each other.
2) Select all the edges of your shell, then deselect the outer edge loops, so only the edges that should be joined together are selected. "Move and Sew UV Edges" will sew all your unitized UVs into a strip of squares. In your case you have a loop, so you'll need to deselect an edge where you want the seam, too.
3) From these even strips you could use scaling and grid snapping to fit them to the UV space. For me I used Polygons > Unfold with a horizontal constraint to deform the UVs to fit the geo better while keeping a nice horizontal shape.
3DCoat is great but sometimes you won't want to go into it for stuff like this, and this a technique I'm super glad I know now in Maya.