Yes, sorry, I don’t know enough about what is behind those choices to be much help on how to better implement. Also, I’m not yet aware of the what is behind the proxy service working to offer much advice on how to better integrate your needs. I will say that maybe now that you have it closer to working and know some more of what is involved in making your situation play along with MyBinder more, you may ultimately want to craft a new post here asking for advice. You may attract more interest than the current topic/title. I think the category of Binder (/ Jupyterhub?) would be more appropriate for that unless I am missing something. I don’t think you even need JupyterLab per se? I think there is a ‘repo help needed’ sub-topic although I don’t know if that would catch the eye of those well-versed in the server proxy.
Plus, there is a Jupyter Community Call in a couple of weeks. Even if you aren’t comfortable making it a topic of discussion, sometimes there’s some time for a bit of technical talk before or after with others that know a lot and can help you that last mile.
Yes, we are one of the snowiest cities of our size.