Made enough progress to be worth posting an update. I received all my lamp components, which I needed before I could make some final decisions about the base and the support blocks. You can see in the layout photo, I ordered some brass bent tubes and couplings so I could route the wiring into one corner of the box, while at the same time putting a small night light in the center. I did that to avoid having a shadow across one of the agate slices. On hindsight, I probably could have saved some money and simply got a piece of 3/4" X 1/8" bar stock and bent it into a square 'C' shape with the long dimension of the 'C' equal to the inside height of my boxes. Drill holes at each end, run the tubing thru the holes at the top and bottom of the box, trap it underneath the hickeys using the lock rings and nuts. Then when I pull the wires, I could simply cable tie the wire to the bar stock. The wires don't need to be in metal tubing.
Next I worked on the base. I needed to figure out where the 3 way switch would go and how I would run the cord out of the base. I also needed to make a large enough recess to accommodate the wire nuts when I make all the connections. My bases are a piece of 3/4" MDF and a piece of 3/8" plywood, covered with 5/16" mahogany. So I drilled a 2 1/2" hole through the MDF and plywood to provide the space for the connections. I routed a space for the 3 way switch and a groove for the wiring. I drilled a 1/4" hole in one side of the base for the cord. Then I cut my miters and glued the sides and top onto the base. Next is sanding and rounding the edges and applying finish, etc.
I also needed to make the support piece that goes between the base and the box, and the top spacer which goes between the top of the box and the main lamp socket and harp. The top was pretty easy to figure out once I had my top tubing. I think I'm going to route a cove around the upper edge of that piece before I finish it. I played with various heights between the base and box and settled on 2 1/2". That leaves room for the easy access to the 3 way switch knob and seems to provide good perspective relative to overall height. I had to cut off my bottom threaded tubes. I think I'll also make the base about an inch wider than the block at the top. To do that I'll cut the same mahogany block as the top, but I'll glue a piece to each side to make it wider. The supports in the photo are just scrap cut to 2 1/2" so I could see what it would look like.
So far, I'm liking the way it looks and fits together. My concept right now is the base, lower support block, and the bottom of the box will all be glued together. The top of the box will not be glued, it will be held in place by dowel pins and the threaded tube that runs out the top. That way I have access inside the box when I need to change the light bulb. Haven't decided whether to glue the upper block to the top of the box or not.