Wrong. By this evening, it was in serious running-on mode. So after jeff_duntemann and Carol dropped by for dinner, I decided to replace the flush assembly. Fortunately, I'd already bought one for just this purpose.
Unfortunately, the connector from the valve to the toilet was being so singularly uncooperative that I ended up heading off to the hardware store for a replacement. It was the original one that was installed by the builder, so I guess it was due to go.
The toilet seems to be working correctly now.
And I'm keeping my fingers crossed. :)