I've decided . . .
cashs_mom: I remember those blankets, and now that you mention it, I do remember the satin wearing off, too. I think they were pretty old blankets, over 10 years, but your point is a good one.
meyert: What's fray block? This sounds like something I need. Those are awesome satins on fabric.com. It gives me all kinds of pillowcase ideas! Did you know you can return cut fabric to them, and get a refund? I did it last week, because the photo was so far off from the colors I got, and that's $10 I can put toward something I like better.
Everyone: I gave the quilt a good hard look, and I'm thinking I'll just bind it with fabric after all. I loved the feel of the satin edging on the blankets cashs mom was talking about, it was so comforting. Big fuzzy, slightly rough blankets, with 2 inches of smooth satin for contrast. My blanket from those days pilled like crazy, but the satin made me keep it longer than I should have. They were great.