@t_smith5
When you have a simple of piece of geometry, such as a ring or collar, the tidiest option seems to be having the outside and inside as separate UV islands.
If you are doing your texturing in Substance Painter (which I think you are from previous posts of yours), then there is no reason to worry about "tidy" in your UV layout. Just divide the collar into smaller sections to better use the UV space. The only time I maintain a continuous length of a UV island is when I am not using Substance Painter and need to place a complex texture manually in photoshop over the UV template. Even then, I can usually find a good place to break the island in 1 or 2 places and make better use of the UV space. It is still organized enough to follow where the islands are, so you haven't really lost anything meaningful but have gained better use of the UV space.