Since I have a top-load washer, I opted to soak the fleece in hot water with a bunch of laundry detergent and Clorox free and clear stain remover and color booster. You don't need these exact chemicals, I think just about any kind of chemical/detergent treatment will help strip the fleece of its waterproof coating. Just make sure everything is "free and clear" and that you put a lot in with a smaller amount of water so that it's really concentrated.
I just let everything mix in well and then hit "stop" on the washer and let the fleece soak for as long as the water stayed warm (it was like 4-6 hours). Every hour or so (just whenever I thought about it) I'd go re-start the washer for like 30 seconds just to let the agitator mix everything up again. Once the water had cooled down to a warm temperature, I let the wash cycle finish. Dry completely on low/delicate heat. Then test the fleece to see if it's wicking. Test on multiple areas of the fleece! For some reason, some areas of the fleece may start to wick before other areas.
Some fleece wicks faster than others, I'm convinced, maybe just because it's different quality or is prepared differently to give it a stronger waterproof coating. I've found that plain, solid color fleece seems to wick the fastest. Some of the super-cute pattern fleeces seem like they take forever! Anyway, using the formula described above, I was able to get three huge, solid color fleece swaths wicked in about 2 cycles each. (I think I did each of them again one more time after that, just for good measure.) Got them all done over a stay-at-home weekend.