I have found that after skirting you can do a simpler cold water wash than NFCo suggests, in rain water if you have it, which removes enough muck and smell to help the fleece survive a few years storage. I then pack the dried fleeces into clean woven polypropylene sacks, tied tightly, and hang them in the barn, where it is cool and dark but there is circulating air. I would only store a thoroughly washed fleece in plastic bags.
The main dangers in storage are moths and rot. As long as the sack is tied very tightly (folding the top over and tying again is a good idea), and there are no holes in the sack, you are safe from moths. Never storing the sacks on the floor, and making sure there are no drips or other damp, will make sure your fleeces don't rot. Polypropylene biodegrades in sunlight so keep in the dark or you will soon have no sack
2 or 3 years storage should be fine.