I have got my sails looking brighter and whiter soaking them in Oxyclean. I would probably get a wading pool to do it outside, with a plastic top buffet table (you know the ones with the molded resin plastic that looks like a Suncast plastic shed or deck box? Not the ones with a laminate over particleboard top surface. You'll ruin those soaking them with wet sails) to pull the sails up over and examine stitching, holes for repair, and stains to scrub with a brush and Bartender's Friend for rust stains (easy to get oxalic acid with detergent.) Note that if you try to do it in the bathtub, bronze piston hanks WILL scratch a porcelain finish with grey marks. (Ask me how I know!

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Most sailmakers do offer cleaning services. As far as Sailcare goes, many people are thrilled with their service, which also includes repairs as part of the package, which they will provide a quote before work begins. However, I am completely skeptical of their re-resining process. Not sure what it is really going to do for you.
Remember that old sails are usually blown out. They are stretched, and do not respond well to sail controls. Therefore, they will be constantly over-powered, slow, cause excessive heeling, and probably won't point as well as they ought to. Any kind of re-resining process will not put a blown sail back into good sailing shape. Sometimes, you might be able to have a moderately blown sail re-cut for better shape, but for how long?
I think 2 determined people with a wading pool, buffet table to pull the sails up over, and a weekend, can get better looking sails on the cheap.