Brian, I like that idea. DO U have any drawn plans for that ? If not I can figure it out.
No plans or pictures, sorry.
Make your shim, then use your end bars to make a template If you take a sheet of 1/4 inch plywood and cut it to the inside demension of the box by measuring in 1/2 inch from each side, placing the end bars across it and marking a hole (through the eyelet of the end bar) centered on the shim you can drill the holes align you dowels and secure them. the other option, which I prefer is to drill holes in the template the same size as the dowels. Cut the dowels so they are the 19 7/8 inches of the outside long measurement of the hive. then just incert the dowels through the holes and tack the side panels of the shim. The dowels can be glued or tacked in place.
Hope that gives you a better idea.