****Update****
Thanks for all of your sympathy and advice. I appreciate it so much.
I used the Dawn method and I now have a stain-free quilt! I'm beyond happy!
True confession: While it was soaking, I did start a new quilt top and sent an urgent text to my LA. However, now that crisis has been averted, I'll be finishing the new quilt top at a later date.
Geri B - I agree that it seems we have to do more and more to avoid this problem. What is going on?
Again, thanks everyone!