UPDATE: Cat seems to have a hurt foot. I spoke with an emergency vet to get some advice. They seem to think that he can wait for morning as long as he will eat and doesn't seem too lethargic. He objected firmly to riding home with me, so I'm hoping that's a good sign for his general well-being. If he doesn't eat or gets worse, the emergency vet is right down the street from me. It would just be a very difficult bill for a found cat I can't keep.

EDIT: He ate a little and is very angry that a stranger has him in a cage alone in her spare room. I do think he'll be okay until I can get him to help tomorrow. He'll handle care better with some quality food and clean water in him.