Don't make things so complicated!

If you want to install Firefox, get the normal Firefox download, and install it on your desktop (i.e. choose a path which you have write access to)

You only need Admin rights to install system wide or overwrite system binaries.

This works if USB devices haven't been locked down by some kind of IT policy.

While portable apps are promoted for and usually installed on USB drives, they can also be installed on local disks as well, and they don't require admin privileges to do so (from my experience).

I was not aware of that. Thanks! I guess the portable aspect is not quite perfect for their description though?