My lines run aft and, whether racing or cruising, all of the cabin top control lines that come aft are dropped down the companionway hatch. I don't see how that is sloppy - it's far better than stowing them on deck and it's easier for the pit to keep everything organized.
If the halyard stayed at the mast, I would do as suggested above: neatly coiled and hung from a cleat.
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