Thanks ladies for your suggestions.
I think to start I'm going to try Lorie S's suggestion of soaking it in a plastic laundry tub, draining it and putting it in the dryer. It is summer now and I'll be able to do the soaking right outside the back door of the house (which is right by the stairs down to the dryer).
I also had not thought of using the handwash cycle on the machine, and will try a smaller piece to see what happens. My washer only does the full cycle, so I'm not really confident in this, but it's worth a try.
Thanks again.