Wool batts should never be washed in an agitator washing machine. If you take a quilt that has been washed that way to the woolen mill to have it recarded, they call it "the wash machine special" and they will not touch it. I have several wool batts. Over the years, they are the best for warmth.
The best way to handle a wool batt is to make a duvet, a cover something like a pillowcase that is tied on, zipped on, buttoned on, or some such way, so that you can wash the cover when needed, but not the actual quilt.