Here are some more things I have managed to salvage from the sheets. They are just tentatively assembled, not properly fitted, not sandpapered, not glued. It was sometimes hard to figure out which piece I was doing. I was simply trying to see what I had, since about half of the bits were missing.
Then I tried to make something nice. As I have already observed, sandpapering is everything. I worked very thoroughly on this piece. You can still see numbers penciled on the bits - that was very helpful to see how bits fit together. I almost forgot to take the before picture before I started painting.
And the chest joined the bedroom furniture set, and, amazingly, it went just right onto the funny half-circle, as if it had been specially made for it. I still think this furniture is clumsy, but it looks much better when painted.