Are there any suggestions how to seal the exposed edges?
Customer does not have issue with how long it will last is what I hear You say.
As long as it will last a reasonable amont of time. I see you are in Litchfield NH.
If you want to use acrylic use the same procedure as follows only use the sdhesive for the acrylic. However, I would use lexan the material they make outdoor signs with. It stays scratch free and none yellowing for over 27+ years.
Sandwich the item between the two pieces. If it is thicker you may have to use a spacer, so you do not cup the lexan or acrylic. If the item is paper thin just clamp it all the way around using a 1" x 2" pieces of wood, but not touching the outside edges. Simular to a strainer frame, front and back.
Place wood clamps so as not to block the edges.
Then take the Lexan or Acrylic adhesive and just apply it so the adhesive just binds the edges and does not migrate in toward the piece. The same way you do when you glue plexi.
This should hold up for about 5+ years, probably longer than the printing on the paper.
PS I would suggest you tell him to bring it in during the winter to help add to to its longevity.