Hand Tools Archive
Two other things to consider are the tensioning screw, and using the blade hand-held to understand how it cuts.
Rather than by bedding perfectly, a scraper blade gets some rigidity by being curved. Tightening the tension screw behind the center of the blade serves the same purpose as your thumbs in a hand-held scraper: curving the blade to stiffen it, and focusing your scraping on a narrower path. These will help to avoid chatter. It takes a finer touch to get it to work well with less curvature, so it may be helpful to get it working with significant tension first, and to gradually back off if you want a flatter surface.
The other thing I find helpful when sharpening any scraper blade is to try it on wood without the plane. This gives me a lot more feedback on how it is cutting, and I can easily adjust the attack angle as I go, to find where it works best. Some scraper planes allow you to vary that angle, so this allows you to select a good place to start before fine tuning. With a Stanley 80, I would check to see that the angle where the blade works well is close to that enforced by the plane. If not, try changing the sharpening procedure as Derek suggested.