Can you submerge it in a sink full of water and hand-scrub after it's soaked for a while? Maybe scrub around the edges with a soft toothbrush after the Vilene is saturated and soft?
I haven't used this product a lot, but when I use any water-soluble stabilizer, I cut and/or tear away as much as possible before washing. I don't think I've ever noticed any that doesn't wash away.