But the reply from the server to the initial CONNECT is 200 OK, not 302 Found or some other redirect code -- I don't think LWP would interpret that as a redirect, would it?
Also, the 403 seems to be coming from the proxy rather than the remote server. Obviously all the traffic is coming from the proxy, so I can't tell that way, but because the preceding CONNECT is to the proxy server rather than the remote server I would guess the response comes from the proxy as well.
And the text of the HTML page returned along with the 403 response seems to indicate it's coming from our proxy, unless the remote site is running the same type of web proxy.
So I'm a little doubtful of your answer, although I appreciate your help!