The final verdict is that the fork was bent.

I was suspicious not only because of the way it looked when together but also because it had three mismatched spokes on the front wheel when I trued it. I have broken spokes many times on the back wheel of a road bike, but I have never broken a spoke on the front wheel. Furthermore, the reflector on the stem post was missing. The reflector bracket acted like a washer, compressing the headset. Without it, the whole thing was loose. I've seen this before, but I hadn't realized that it could have been related to fork damage.

The shop I took it to knew exactly what to do. I brought it in Friday night, they worked on it Saturday, and I picked it up Sunday. When I picked it up, I used the edge of the counter as a guide, and the fork looked straight. I reassembled it Monday night. The bearing line on the crown race had a noticeable angle the whole way around from being worn unevenly. (I should probably replace the headset, but I am too lazy.)

Together, the Univega looks like it has an oddly backward bending fork, so it's true to its brand, even with a straight steerer tube. Overall, it looks a lot better and feels a lot better.

Many thanks for your help.