Dona, it would be helpful to see photos of what went wrong, to help, and also to learn from you so I won't make the same mistake. Don't cry, you can get your revenge by eating them! To be clear, you are stamping an image on it ahead of time, because it is a curved surface you can't stamp on? Do you need to overlap the paper to get the shape, or can you cut off the extra? Does getting it wet cause problems with the stamp colors running?
I was considering doing something similar, and thought that if the royal icing is very dry and hard, I could use a handful of rice to weigh the paper down. Maybe if it dries while being held down, it will stay the correct shape even if it does not stick as well as I like, without the corners lifting? My concern is that the rice might soak up moisture and stick, or the stamped color will be absorbed into it, blurring the image. Wish there was a way to "set" the stamp... like hair spray but edible, lol!
Julia, you suggested using corn syrup as the glue. Is there any type of adhesive already on the paper that activates when wet? Does corn syrup seep through causing a problem with the stamped image? Does the paper have enough give/stretch that the stamped image might become distorted?
Also, will stamping a particularly wet image after applying it to the cookie make the edges curl up? I would like to do some where the stamp goes off the edge of the paper onto the icing surface. Do they tend to curl more towards one side (such as the shiny side), possibly making it adventageous to stamp on the other side?