Just catching up on the posts and wanted to throw this out there. I agree that the puffy sticker appears to be on a matting, possibly a scrapbook page and is a plastic/vinyl material that kept if from deteriorating.
The "second" sticker whose backing was found in the "special" box is probably what left the residue on the duct tape and it appears to be simply a paper type sticker. Having placed many a bowl etc in the dishwasher with these type stickers what happens is they deteriorate and simply fall apart when in water. And this is only after a one hour cycle! Four months in the elements and water and that sticker is long gone. I think the missing sticker will never be found...but do hope that the residue will tie it to the house.
Or maybe it just is stuck to the bottom of a investigators shoe!!