Before I moved back across the country, I designed and built a heart of redwood case for the clock and set some machine screw wood threaders into the middle section so that the front and back plate could mount together without damaging the wood.
After I assembled it, I used a combination of mineral oil and beeswax to finish the surface to a nice sheen. It's soft and smooth, but not slick. I might do a few more coats to make it really shine.
This is the assembled clock with tubes in. Right before I took this, I dropped (and shattered) one of the Numitron tubes, so I will have to order another from ebay.