FYI I could not get the graphical installer to work behind a proxy at all. There is no option to configure the proxy in the installer and it does not seem to respect the environment variables or the network control panel proxy settings. Running the text installer worked fine and had a setting option to configure a proxy. I am not sure if this helps, but hope it does.
The GUI installer uses the Gnome proxy settings for this and it should also be looking for the environment variables as well. Since the text-based installer works that’s definitely a step in the right direction. Are you able to connect to the internet at all in the live-desktop session?