Fast forward a few weeks and 1 welder later. I obtained a used 20-inch disk from a farming implement. It was quite rusty, but I set my 9-year-old to work on it with an orbital sander, and after about an hour and 3 breaks later, he had it pretty well cleaned up.
After the base had been cleaned, I welded a flange into the center from the bottom. The flange is threaded to receive 1/2 inch black pipe. As shown in the picture, whle the bottom doesn't look great, the top (only part visible), it looks fine.
I had a theory about drilling a hole in the base to allow the cord to pass through. This turned out to be an educational experience, as I maimed the drill bit attempting to even scratch the surface of the disk. Good point to note: Disks are hardened steel, and they are really really really hard. It quickly became clear that I could not drill through the disk, so I cut a notch in the edge with my grinder in stead. Works fine.
The pipe was cut to allow for a 5'7" overall height for the lamp. The lamp is actually much taller than most, but we decided that's what we wanted, so the length of the pipe was cut to 4'7". 5'7" - 2 inches for the base height, and 10 inches for the height of the lamp shade holder.
Shown above, the paint drying. I tried to take a movie, but it seemed to lack plot. Basically, I put it together for painting. I also had to make sure and clean and paint the bottom side in order to protect the carpet.
For the lamp innards, I purchased a lamp building kit for about $8 at a local hardware store. It had pretty much everything I needed, plus instructions. There were numerous kits to choose from, technically, I bought two. One, I bought for the 3-way socket included. Another had some nice spacers that worked as mounts for the top end of the lamp. They made it a very secure press fit, so there was no need for me to weld something on the top end of the lamp to accept the lamp making pieces.
So we wired it all up (had to take it apart first), plugged it in and viola! Finished Product: