Good news! We found his family. Or rather, they found us. On Saturday (yes, this post is several days overdue) I got a call from someone who said that he was at a local shelter looking for his cat. He spoke with the shelter workers and asked if anyone had reported a found cat matching his little guy's description, and they gave him our phone number. An hour later little Bernie, as they call him, was back home with the people who'd been taking care of him.
Kitty had been visiting their house for several weeks, and they'd been asking around to see if anyone in the neighborhood had lost a cat. After a while, with Bernie staying longer and no luck finding anyone to claim him, they decided to adopt him, get him fixed, and have him microchipped. Then, a day or two before he was due to go to the vet, he ran off. (This does not surprise me in the least: I had outdoor cats when I was growing up, and they had an uncanny sense for when they were about to be subjected to a trip to the vet.) They've been looking for him ever since, but only on their side of a rather busy road that divides our little neighborhood. We live only about four blocks apart, but none of us thought that Bernie would cross that road.
Anyway, a happy ending for little Bernie and his two humans, who were overjoyed to see him. I spent about half an hour with them when I dropped him off, and they seem like wonderful people. I'm glad to see him in a good home.