One argument against any kind of twin foresail arrangement is that the tension that can be applied to the one carrying a sail is only about half that of a single stay and this can result in a sagging jib unless it is cut for the purpose.
Certainly, furling a jib is a lot easier and quicker than changing jibs and the time gained can make up for the slight loss of efficiency of a part-furled sail
If you want to keep the hanked sails, I have never heard of anyone stowing the sheets with the sails attached. Normally, the sheets would be left in situ, ready for whichever sail was going to be set, and that sail could be left hanked on and tied up to the rail. Boats with a twin arrangement tend to have duplicated fittings such as genoa cars to make this possible, otherwise you would have to thread the sheets for each sail or use the same ones.
Tacking round the reefer could well be a problem. When both foresails are furling it is common practice to furl the jib before tacking. In the olden days when I had hankable sails I would normally shackle the tack to an eye near the bow, though in some boats a short wire strop is used if it is desirable to raise the sail a bit.
Far away is near at hand in images of elsewhere