Try putting them in plastic pill boxed. Put a bit of tape on the ends and stick it to the side of each compartment. When you open the box , grab the taped end and lift it out. Get a small travel pill box. And try and keep it upright.
Im not entirely sure how to explain this but Ill try lol so I lay the necklace out so it's one big loop, then I twist it and turn it so that it's another loop (kinda like when you tie your hair in a ponytail), keep repeating until its as small or as big as you want. Once you're done with that take a rubber band and loop it around the multiple layers of the necklace (to keep the loops from coming undone) don't know if that all made sense lol so if you didn't get it just ask and Ill try to explain it more clearly!