I would recommend soaking in a product called Restoration. It is made specifically for vintage and fine fabrics, and will take out many, many stains. I would deal with the stains before putting any time or effort into finishing the top. You can soak it in the washing machine, just do not agitate at all. Put the Restoration into the water to dissolve, then add the top and push it all down into the water with your hand and let soak---all day or night is ok. Spin it out, then add rinse water, and let that soak, again, with NO agitation. Spin that out and do another rinse the same way. If possible, lay flat to dry (outside ontop of a clean sheet in the shade, with another clean sheet ontop of it if it's under a tree and birds may dirty it). If that's not possible, hang it over a clothesline to dry.