The screen would be great but I know the hot glue won't hold up to weather. It's a lot like ceramics or pottery, there is a chemical change that causes it to contract and expand in hot/cold weather. The fluctuation makes it pull away from what it's touching. It might stay on the screen, but I think it might pull away from the pennies. Of course my experience has been in KY weather. Might not happen in Florida or in the NW where the weather is not as extreme in one way and then in the other.
Great thought about the screen, though, Elaine!