This is my finished lamp. When I applied the acrylic varnish to the front piece, the moisture caused the veneer to curl up quite a bit. It wouldn't have been to difficult to straighten out if I added a tiny bit of support to the side seams and some "Eco Glue" (which is like a super strong and very tacky white glue, I found it to be very useful.), but when I positioned the back piece which did not have any varnish on it, I realized that it made a nice design. So I decided to abandon the side pieces and leave the back piece unvarnished so that it would keep its shape.
This is the lamp turned on.
The shadow of the base does show, but it depends on the surrounding light. I am glad that it does not give off a very strong contrast. I also cut one of the knots into the shape of a water droplet and put a piece of fabric behind it. Madrone burl is very easy to cut by hand with a pen knife, but I could never manage this on other kinds of wood, such as walnut, as that cracks very easily. This was a really fun project, and I don't know if I ever would have gotten around to working with veneers if the requirement had not been that we have to work with something that is new to us.