Something I'm sure some of ya'll are already doing, I just haven't stepped back to watch what I'm doing with anchor rope.
In the past I would store anchor rope neatly coiled and tied. Even to the point to wrap Velcro straps around them to keep them neat.
While washing the ropes in a 5 gallon bucket of water, it dawned on me, just keep the ropes in an open container. You can transfer them, access them, do just about anything you want and don't have to worry about tangles, knots, etc.
What I've got is a 100', 1/2", primary anchor rope in a holder ready for deployment, then the secondary anchor rope, throw line and dock lines in the other container.

They are stackable, you can wash the ropes in the container and then store them.