Why Django 2.2? That version is no longer supported, and I'm guessing there's some technical reason you are using the obsolete version? (Production Django is now on major version 4)
But if you want Django 4 and Python 3.11, here is some info copied from the website:
3. Newer Python and newer Django? It is possible to have a djngo.com with Django 4 and Python 3.11. Solved by aghgamut who was the first to port Python to Cosmopolitan. Please note that this Python and the one that djngo.com use are different, the later has been heavily optimized by jart to run well on cosmo, the former is as close as upstream as you can get. Choose your destiny.
Python 3.11.0rc1, Django 4.1.7. I think ingenieroariel also has a binary available on the website.
It's a proof-of-concept (because I wrote it just a few hours back), but it shows that we could have the latest version of Python+Django packaged in a single-file executable. Someone could definitely improve upon the build process (like it was done for Python3.6) and add more packages if they wanted.