When I was younger we were poor, as in no running water poor. We had many meals consisting of potatoes. What my dad did to keep them was dig holes about 3-4 foot deep and about 2 foot around. We put straw in the bottom then potatoes and another layer of straw. This ended up with around fours layers. Our yard typically had about six of these.
Now we didn't have whole potatoes in every one of these. About four or so had the eyes in the hole. (eyes are the seeds of the potato.) When you buy potatoes at Wal-mart or wherever the eyes are on the outside they are little nubs. We got ours at a farmer's store and we ate the potatoes and planted the eyes. To prepare them when we peeled the first few and canned several we would cut the eye off and a bit of the meat of the potato. All the peels and the bits went into the hole with the eyes. The same method was used to plant them. A layer of straw a good amount of peelings eyes with a chuck of the meat connected to the eye. Another layer of straw on top of it. and again we used about four layers.
None of these had fertilizers or anything. They were just planted in the aforementioned manner. We dug holes in different spots every year, not reusing the same place for a couple years. I would say that if you had access to a wooded area or large open areas this method would work fine. Thinking about it you could also use this method in a couple places in your garden. Digging the hole and adding the straw would make for an extra bit of tillage and fertilizer for the garden as well.
I've also heard of growing them in burlap or similar bags. That method works the same way except instead of planting them they get put in a warm garage in the bag. Some things I've read say to plant about a 2" chunk but I'd expect that you could use the peel and a smaller chunk.
I am not in a situation to put it to the test but while there isn't anything major hitting at this exact moment you might try this method out to see if you could do it. Let us know how the experiment works. - Willie Pete