Thanks to all for the advice and tips! I think I'll try the Dawn-and-bathtub method, since I have a front loading washer. The quilt actually doesn't look awful with the bled-in color; after it dried it's a rather attractive beige.
And since all the pieces cut from the yardage are now the same color it looks like it *could* have been a deliberate color choice. However, it's not what I intended so I know I'll wince every time I see it. Cross your fingers for me!