I have Apple's Developer software installed on my drive. Inside the /Developer/Applications/Utilities folder is an application named Syncrospector. I don't know much about how this utility works. But I know enough to launch it and click its Sync button. That did the trick. I immediately checked back at Entourage and iCal; all the duplicates had vanished.

The entire process, starting with iCal Duple Deleter, should only take about two minutes. There are probably other variations on this theme, perhaps simpler ones, that would have worked as well. But this is what I tried and it worked. Having a way to prevent the duplicates from appearing in the first place would obviously be a preferred solution. Until then, this will do.