It would be nice if the test data included these parts:
I would modify my green group that gets the longest edge to make sure it is “horizontal” (parallel with the sheet seams). That would handle the pieces in this image that have such an edge already, and in those cases the long segment from Convex Hull would not be parallel to the seams so it would be ignored. With this small change, these “corner pieces” that have two square edges would be handled properly.
That leaves the issue of nudging the post-processed curves in Y to avoid small slivers, however that is defined. My Rhino file ‘Units’ are inches which makes the sheets 55 inches by 120 inches (10 feet), and the boards 5.5 inches between seams, is that correct? What is the minimum “sliver” dimension in the Y direction? Say 1.5 inches?