This -- "Python Version: 2.7.9" is also a problem for recent Mailman 3 (since 3.1 IIRC) -- Mailman 3 is only supported on Python 3. I guess this is Postorius and it's still OK for 2.7 (upgrading to the most recent Python 2 version, which I believe is 2.7.11, is probably a good idea, as there were security issues in 2.7.9 and 2.7.10).
I would guess that your proxy simply isn't permitted to access the REST port by the server. Check firewall settings and try a simple client such as wget or curl from the Mailman host. If you get the same result (ie, 403 Forbidden) with those clients, then you're going to need to talk to your local administrators about how to configure the firewall to permit Postorius to talk to Mailman.