If you are using the ArcMap application rather than the ArcGIS Pro application of the ArcGIS Desktop product then I believe you will need to use the ArcPy that installs with ArcMap and that requires you to use Python 2.x.
To return to this question, I ended up giving up and configuring the users' computers myself so the script could run on double-click as a .py. As Vince said, it's a stubborn licensing issue with arcpy.
For passersby who may be interested in accomplishing what I could not, this may be a helpful resource: https://community.esri.com/t5/python-questions/using-...
Pyinstaller should be able to do this for you as long it was installed in the same environment as the dependencies (modules/libraries) for your script. Pyinstaller finds all import statements in your script and can compile everything into a single .exe file.
Since you're on Windows 10, search for "Python Command Prompt". This will open a window with the current default ArcGIS Pro python environment activated. Pip and other python modules should work normally, as well as conda.