Oh my goodness! DebJMills, by looking at the sealed cones I was able to see what I couldn't see/feel on the opened ones. I have vision issues and the base is rough enough that various things caught my fingernail explorations.
Thank you so much! This will help prevent the tangle and regular maintenance I didn't want to deal with. Am still going to look at those drawer organizers.
My cat Tomas, he could take a loose end of thread and run it hundreds of yards this way and that and all through the house. A spool with the thread secured wasn't so much fun, eventually they all ended up under the couch. But.. a loose thread coming out of a drawer was something like out of a cartoon.