daisy_knotwise and I discussed how to repair this. Today, I went to Home Depot and got four 17 inch long 1 x 6 oak boards. I glued them into the bottom sides of the bookcase and now the failing shelf rests happily on top of them. Since there's a bit of a decorative lip on the front of the bookcase, the boards fit entirely inside the lip and are pretty much invisible without a close inspection.
While I was there, I decided to pick up one of the Cree 100W LED soft white bulbs and one of their 100W daylight LED bulbs and stick them into the light fixture in my office in the hope of getting reasonably balanced color. This seems to be working ok, but I won't be able to tell until I can get the fixture cover back on. The bulbs are a bit larger than the old ones. Oops.
I can adjust the position of the plate on the nipple that the fixture snugs up to, but not without some penetrating oil to loosen the nuts, which are pretty firmly stuck right now. And since I'm going to go freeze at tonight's Cubs / Cards game, that will be a project for a bit later. :)