I have several stackable clothes dryers that I air dry my fleeces on. When I use them I stack an extra one on top so my in house furry friends dont lay and play with the fleece(well at least not nearly as much<grin>, if at all). When I use these the do take up some space, but they are collapsible for storage. They are essentially a square plastic frame with legs that a big piece of nylon netting(like the lingery bags are made of but with a finer mesh). The good thing about them is that if it is nice outside I can put the whole thing outside and bring it back in when the weather changes or night falls.
The best air dry I have really is a broken expandable baby gate. Its two screens of plastic mesh with square wooden frames. There used to be a wooden arm that went across the middle to make it expand and put pressure in a doorway to hold it up, to but that is what broke so it was not longer useable. I just sandwhich as much of my washed fleeced between the two screens as I feel good about. Then I can move it anywhere, near a heat vent, outside in the sun, by the wood stove, etc.
I think the most amazing fleece drying set up I have seen belongs to a lady I know. It was built out of 2x4's and was a stand that went from floor to ceiling. The stand was placed over/around the wood stove. She had it built quite wide so it was no where near the stove. There were multiple frames with mesh screen that were shelved in the stand above the top of the stove(a few feet above the stove). There were runners so she could just take the frames in and out. She has lots of Angora goats and sold yarn, fleece and locks in large quantities, so she processed stuff in large quantities. It would work for form someone who was just processing fleece every once in a while, but it did make my mouth water to see all that fleece drying!
I wash most of my fleeces in my top loading washer. Just let it fill with the hot water, put some Dawn in it, turn the washer off and set the wsher for the spin part at the end of the cycel. Then submerge some dirty fiber in the water, let it soak until the water is just barely warm(so the "grease" doesnt settle back on the fiber), and turn the washer on to spin water out of the fiber(it gets pretty dry). I usually do two Dawn cycles( think its about a 1/4 cup of Dawn) and at least one rinse. I have also used my washer or a salad spinner to spin the water out of fleece I have washed by hand. The only fleeces I dont wash or spin the water out of in the washer are ones that I want to keep the lock formation in for tail spinning. The washer is a lot more time effective me than washing every thing by hand like I used to.
Oh! I just looked back, sorry this is sooo long.....