Les (Lori's father) drove the car there from his house, with me following behind in his truck. The noise stopped for him in mid-drive, which made me worry that the mechanic wouldn't hear it. But when we took a ride with the mechanic, it came through clearly.
The mechanic called me a couple hours later. He confirmed with a stethoscope that it is indeed in the transmission. So fixing it involves disassembling the transmission, removing the errant piece, and flushing out the transmission so that any remaining metal filings go away.
Their estimate: $1,900-$2,300.
So I called the Honda dealer and asked them for a ballpark price, assuming that everything said by the transmissions place was correct. They don't repair transmissions; they replace them. Their estimate: $2,500-$3,500. (And when I mentioned that we were dealing with Transmissions by Lucille, the Honda guy said "oh, they do excellent work.")
So Lucille got our business.
We can afford it; we've just recovered from the income tax hit. But this continues our five-year difficulty with getting ahead.