"Cleaver-Land" has got to be one of my favorite plays on a prewar name that I've seen. That's so perfect.
As for the rest, I don't think there's a problem or need for an edit. You never said that he was in a desert. And Autumn in Missouri can fluctuate between pleasant and brutal. If someone is limping for miles in a full kit while wounded on a warm day, the extreme humidity in the area (particularly before a storm) will most likely kill him -or get damn close, as you depicted well. Sinbad is a very, very tough bastard, or he probably wouldn't have made it at all.
Not having water isn't an issue either. People get lost in the woods and die of dehydration within miles of fresh water in the real world. Even if the rivers and streams of the area aren't particularly radioactive, Sinbad is a nomad from far away who doesn't know where they are. It would be very dangerous to stray from the road to search for one in his condition.