Rick:
I'm going to keep using it at the lower resolution, because that's just going to make things so much simpler in the long run. It's a work machine (purchased by my employer), so I'm not too concerned about an imperfect display, despite the annoyance.
But the plot has thickened. Over the weekend, I bought a new, almost identical, iMac for personal use at home. I brought it home and checked the display very carefully, anxious about the possibility that the issue would be replicated. I'm happy to say that I tried the monitor on the new machine at several resolutions, and they all look beautiful! Now the (flawed) work machine has ATI Radeon graphics while the one at home has the (less expensive) NVIDIA GeForce, so that could explain it, I guess.
Thanks for all your tips!
Evan