Wait, take that back. I just removed squid from the picture and I'm getting a lot of hung children.
I think squid timeout settings helped.
Edit: I'm not sure if that was the case. I looked again and the 80 hung children were all from one IP. I think a misconfiguration client or a bot was causing what I was seeing, as it has cleared up now. I'm going to have to let this run a lot longer before I can say anything for sure.