I agree with Mike. Cones are made to pull the thread off the top. You don't want them to spin. If yours is spinning there's a strong chance that's the source of your nests.
You can probably make a workable cone stand out of a piece of wood for the base and an old wire clothes hanger with a small loop in one end. It doesn't take much.
Don't make it too tall. I did on mine and the thread likes to jump out of the open thread guide on top of my 15 cone.
Just tall enough to clear the top of the machine will work fine.
Rodney