Installing the veneer strips didn't quite go as planned. My initial idea was to apply a little contact cement to hold the overlapped end in place. This would have provided plenty of hold once the overlap was pressed into the rib slot. The problem was that before being moved into the slot, it was difficult to keep the ends from springing apart on the tightest radius strip, and I split the veneer. I abandoned this approach and as I was removing the damaged strip, I damaged it further.

I decided to just try skipping glue altogether and see how that works in the long term. The overlap is snug in the slot, so I don't expect it to shift much. If I end up being wrong, it will be easy enough to separate the lamp from the socket fixture and fix it.

But still, that tight radius hoop is difficult to feed through the slots. I ended-up splitting another strip of veneer as I was fitting it into place.

After the tight radius hoops were installed, the others were comparatively easy.

After seeing this photo, I had to go check the lamp - the overlapping ends are under the nearest rib, and the center veneer strip had been cut narrower on one end.  How did I manage to do that?   Fortunately, I've got plenty more veneer.

One lamp assembled and ready for a socket.