I would skin the back and the one inaccessible side with 1/2" ply. .. glued and screwed every six inches all the way around. ... dining the top and bottom will do nothing for the whole stand twisting/racking over... is that 36" or 48" square?
At 36" or 48" I don't think I would fear too much about removing the centre brace on the side. .. it's there anyway you can double up the top spanning member like it is in the front?