Can you use something like the "Tide to Go" pens or a bleach pen (controlling the bleach movement)? Or some kind of spot remover - like a carpet or furniture spot remover?
That's assuming you don't ever plan to machine wash the quilt.
If it were me, I would use the spot remover, then grab the Woolite and hand wash the quilt in the bathtub and lay it on a tablecloth to dry flat, if your washing machine and dryer can't handle that size quilt.
Let us know how it turns out, either way.