I finally settled on the free Simple Floating Clock. It does optionally allow you to pass mouse clicks through the clock, but it still takes up visual space in its default layout.
Solution: Open the app's settings (by Control-clicking on its face). On the Colors tab, set the opacity of the face to zero. Now you can make the clock as large as you like, and only the hour markers (pips) and hands take up negligible space. These are so small it's as if the clock wasn't there. The face doesn't exist, so you can click through it whether you choose the "pass clicks through" setting or not.
You could even enlarge the clock to fill the screen and it wouldn't get in the way of your work. Personally, though, I leave it in the lower right corner. If you do want to change settings, carefully control click on the hands or the pips to open the settings dialog.

