That is an awesome idea. I love it!!
I was having the same problem, plus, I really wanted to keep my wound bobbins together with the thread. I bought a June Tailer thread organizer at Michaels, replaced the short dowels the organizer came with, with longer ones (they easily popped out) and then was able to put each thread on a dowel with a bobbin on top. If you're handy with a drill, my mother-in-law has a bobbin organizer made from a simple piece of wood and some wood dowelling. Simply drill holes in the wood, cut the dowelling to a good size, and pop the dowelling in. The dowelling is high enough to hold several bobbins and then they never go missing.