I'm still just dry fitting here in order to see how things would look with a light inside.

The original plan was to mount the socket on the interior of the lamp (with the 3/8" lamp rod through the top cap).  However, I found that with the sockets I was using, this would place the light bulb too low in the lamp, past the mid-point and closer to the bottom.  Since the sockets also support the European-style mounting (the big ring nut), which puts the socket mostly outside the lamp, I re-designed the top cap to mount the socket that way.

 

This did have the intended effect of shifting the bulb up to a better position - not exactly in the center, but close enough.  I wired it up with some lamp cord for a test lighting.

Time to disassemble and do a little sanding.  Given the height these lamps will hang, I'm freed from the tyranny of the perfect in that respect.