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I have 2 Blue Performance bulkhead sheet bags from WM mounted to catch the lines, a smaller one on port where it's just my main sheet, and then a larger one with winch handle pockets on starboard where it's the main / jib halyard and boom vang which all come through a set of clutches and back to one winch on starboard at the front of the cockpit.

Coiling the lines and stowing them in the bags after raising the sails isn't an issue, and they work really well for keeping the lines out from under your feet while underway... Since I'm on Long Island Sound, most of my tacks are usually fairly long (sometimes 4-5 hours between tacks if the wind is just right and I'm trying to get somewhere) so I might get a small set for the Jib sheets for next season, but they aren't in the way like the halyards and sheetline were...

EDIT:
Link to the bags...

 

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Large loose coils over the respective winch. I would think that would take less time them stuffing them in a bag.

Since they all go through a 3x rope clutch, and then to a single winch for those lines, I can't use the winch to hold the lines (I DO coil the lines up over the winch at the dock when the sheet bags are stored below).

Will they knot up coming out of the bag? A large coil ready to use, and then placed on the floor will run freely compared to a bag I woutld think. How big will this bag be?.......i2f

To "stuff" them in the bag, I coil them up, and while holding the middle of the coil, just push the center down into the bag. The loop ends stick up the sides, and it pulls out still coiled without a mess. As long as I pull the sails down in the opposite order I put them up (aka Genoa was last up, so first down, this is because both halyards share the same bag and one gets "stuffed" on top of the other) I don't have to do anything special with the lines and they just pull out of the bag neatly without tangle.

 

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Very interesting on your procedure to place the line in the bag.......i2f

simple but effective...

now if only I can keep guests on trips from using the sheet bags for holding bottles of water, cameras, empty beer bottles, etc... I can actually pull the lines out without being snagged by a corona @ a nikon stuffed in there 3 hours before by someone too lazy to go down below.