An index card worked!
Unwilling to use a knife to bend my wife's 24-inch iMac, I tried a 3 by 5 index card. Just slipped it about half-way in and bent the part in my hand to the front, hoping to thus angle the part in the machine behind the disk and thus guide it out. And it happened!
As soon as the disk began to peek out of the slot, I quickly slid the index card out, and the disk continued its normal leisurely exit. I surmise that the disk was somehow hung up inside the drive, not hitting the exit slot correctly.
I didn't even have to press the eject button, because the Mac had been trying every few seconds to actually eject the disc, since my wife clicked the eject button. The disk unmounted, but it would not eject. Every few seconds, the drive would make its ejection sound, but the sound would abort with a clunk. I tried a number of other remedies, including restart with the mouse button pressed, etc. None of the software remedies had a chance, because the disc was not visible to the software. Disk Utility saw the drive, but just kept waiting for the disk.
Hope this helps someone. My wife's iMac is under warranty, but it's heavy and awkward to lug into the local Apple Store, which is in the center of the area's biggest shopping mall.