I would quilt and bind the top before attempting to remove stains. Wash first in Synthrapol to make sure none of the dyes bleed, then follow directions at
http://www.retroclean.com to remove the stains.
It's risky to wash a top that has not been quilted, especially since fabrics can shrink in different ways. This can result in a distorted top that will not iron flat. Quilting prevents fabrics from shrinking so radically.