This is total overkill but you could ...
Build your cabinet side panels out of 5/8" material, then lay down the art, then cover it entirely with 1/8" acrylic, and use 3/4" t-molding (5/8" + 1/8" = 3/4")
This would protect your side art forever, and the sides of your cabinet would be shiny and smooth.
I think that would look so cool !
Dig it?
Craig