With this patch, I continued to get the following error 
SSL23_GET_SERVER_HELLO
Until my coworker finally found a fix posted by Philippe Biondi:
+++ b/mercurial/keepalive.py
@@ -237,6 +237,8 @@
              else:
                  # no (working) free connections were found.  Create a
new one.
                  h = http_class(host)
+                if hasattr(req,"_tunnel_host") and req._tunnel_host:
+                    h.set_tunnel(req._tunnel_host)
                  if DEBUG: DEBUG.info("creating new connection to %s (%d)",
                                       host, id(h))
                  self._cm.add(host, h, 0)