I wrap mine around a piece of cardboard and store them in a tote.
Wrap them around a large can. We use out oatmeal cans. Wrap a grocery bad around it and store in a plastic tote.
Just a thought. How about an old picture frame. Wrap the cord around in a figure 8 pattern so it doesn't slide off. Kind of like you might wind the electric cord from a vacuum cleaner
Wrap them around pool noodles, then store upright in a large trash can.
a reel/wheel of lights.