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I don't have a recipe for you, but I highly recommend using Pomona's Pectin. It's actually made from apple pectin, and it allows you to use less sugar. If you're set on not using pectin, though, you might just try cooking the jam longer until it "sheets" (comes off a spoon in a sheet rather than in droplets when held over the pan) off a spoon. In any case, the grated apple is a clever idea, and it wouldn't add much, if any, flavor to indicate that you used apple at all. Good luck and let us know how it comes out!