Forepeak w/o cushions - I fold my sails. Spinnakers in laundry basket or turtle.
And you say you're cruising
? Where do you put all your stuff?
On my boat, I'd really be hard-pressed to find space if I didn't have my headsails on furlers. My trysail usually lives on its track at the base of my mast, I have all I can do to find space for the storm jib, asymetrical, and Code 0...
With that sort of inventory, and depending upon how flat your new asymetrical chute might be, you really should consider a Code 0... No other sail will so often make the difference for a cruiser between sailing and motoring, and they can be furled tight and stowed in a very light, compact package... No other sail offers a higher ratio of horsepower/storage space required than a Code 0 on a furler, and yet I'm always surprised how rarely I see them on cruising boats... Many folks won't bat an eye over spending $2K on something like the latest and greatest chartplotter package, or a 15hp engine for their tender - but apparently a similar expenditure for sails with the impressive utility and versatility of free-flying light air sails is difficult for most to justify...
My hat's off to anyone who carries and uses that sort of headsail inventory... Hell, half the time I have trouble making the effort to simply furl my RF genoa
to effect the equivalent change between a #3 and a #4 jib, I can't imagine actually performing a headsail change to do so... (grin)