Why have plywood verticals? Get something like this instead and use pillars. Paint the lower unit under the glass in black.
Straight answers from thirty years in the business.
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Look at woood working sites for edge banding. Something like this http://www.rockler.com/wood/edge-banding
I was going to suggest the same, there are lots of very thin veneers that just stick or iron down. This is very common with plywood pieces. Or like Duane suggested go with something besides plywood.