Check with your firewall expert. They open the firewall for PROD servers so there is no need to use the Proxy.
Thanks your tip helped me solve my problem:
Had to to set the Credentials in two locations to get past the 407 error:
HttpWebRequest webRequest = WebRequest.Create(uirTradeStream) as HttpWebRequest;
webRequest.Proxy = WebRequest.DefaultWebProxy;
webRequest.Credentials = new NetworkCredential("user", "password", "domain");
webRequest.Proxy.Credentials = new NetworkCredential("user", "password", "domain");
and voila!