Try putting them on a feeding schedule where their feed gets placed in the coop shortly before dusk. Don't starve them but make sure they are wanting the feed you serve and will come at the end of the day when they know it will be in the coop. Then just close the door. But free them when the sun comes up!
You ask if they will be too cramped. Depends on whether they will be confined to the coop if snow falls in your area or have access to the outdoors at all times. If they will be spending the winter inside, then yes, you have way too many birds for that small a space. Get rid of 5 or 6. If your climate is such that in the dead of winter they will use the coop to sleep in and still have the outside world to spend every waking hour in, then the coop as a dormitory is probably ok. Time will tell if they will use your nest boxes. If they don't use them from the start, I think you will have trouble encouraging them to do so when they get used to laying eggs under the porch, in the back seat of the old DeSoto or in the hollow log down by the creek.
If you had an adequate space for your birds, I'd suggest confining them until they learned what the boxes are for, but with too many birds as you have, it might just cause some nasty problems in the flock.
Perhaps you can build a temporary outdoor pen to confine them during the early egg-laying period? It's not the most inhumane thing you could do and they might get used to laying in the nests (or at least in the coop.)
(No experience with truly free-range hens. Here, "free-range" is synonymous with "fresh chicken buffet" for raccoons, fishers, coyotes, hawks and eagles.)
Wayne
