Filler is what I was thinking but it would have to be silicone I guess.
I prefer to have the overlay over the plexi because the textured material feels more authentic than plexi. (early 80's authentic as opposed to whenever "plexi over art" showed up.)
The 4 screws that hold down the "artwork/plexi" layer to the plywood would be the only 4 potentially noticeable. All other mounts will be under the plexi. If that makes any sense.
I'm still convinced Kelsey's way is the cleanest solution and I was just concerned about the 4 potentially visible/wiggly

screws.