Stalled connections show a client request but no HTTP response

Have been discussing this one on IRC but wanted to capture everything here since it seems like a fairly serious issue. Since upgrading from 5.3.2 to 6.1.1 we have witnessed connections that, from the client perspective, seem to stall after the client sends the request. TS logs the connection only after it seemingly hits proxy.config.net.default_inactivity_timeout (5 minutes), but logs a response code of 000, despite the presence of a request (e.g. GET with a request URL logged).

For the time being we have failed back to 5.3.2 but I was able to capture a sample of this situation in the slow log. This paste shows the slow log as well as the corresponding squid.blog entry (default format).

This issue feels similar to TS-3456 but we are not using tunneling, though we are using SSL/TLS in this case.