I try to tap a diaphragm against the lever after adjustment. I think there should be about 1/2mm separation. If the hex is too tight it will lift the lever right against the diaphragm, so that when you screw the faceplate back on, the poppet wants to lift due to elasticity of the diaphragm.
I was surprised by how floppy I thought the lever was, and was initially concerned I wouldn't get enough poppet lift. But I was wrong. Instead, I had the same trouble you did.
I haven't tried a rattle test, but you can imagine what 1/2mm might do. It would be pretty subtle. But the point is that there has to be SOME separation.