If newspapers are stacked on top of each other, then packed into a strong frame, like a milk crate, would that make a good backstop to shoot into? The newspapers would be struck on the sides, now on the face.

I would think that they would make a good backstop in the sense that arrows fired from most bows would most assuredly not pass through it (assuming it is packed very tightly). However, arrow removal from the target may be difficult as I would think the thousands of thin layers will offer resistance similar to a more solid, "one piece" target as opposed to some of these foam, multi-layered targets found on the market.