I love RetroClean and use it all the time. It sounds like it's really dirty if you don't want to work on it until it cleans up.
But I have to ask- are they stains here and there or allover dirty? If just stains I would tie it first, then wash.
If you wash first I would soak it in Retroclean, then dry and tie it. Be sure to use a square knot and tie at close intervals.