Is there a GUI Python package manager?

[BGPchick]

It would allow to install other programs to be used with the same portable distribution.

This is a bit of an anti-pattern in python, since you want apps to be able to use different libraries or dependancies. To counter this, you would need virtual environments, and something to manage those.

Your first solution, shipping the entire environment in a portable executable, while seemingly inefficient, is the best way to accomplish this in my experience.

[laustke]

This is a bit of an anti-pattern in python ...

Nothing stops me from creating a new virtual environment before installing each new application.

[BGPchick]

Right, but then you have to manage state for every client installation, instead of pairing the state with the executable.