Always start with --profile if there is no profiles.ini. Otherwise,
firefox will create and use the profile for the first start only, but
not set it as default. It would create a new profile on the second start
then.
Instead of trying to override the .desktop entry of Firefox by
installing the custom one and adjusting XDG_DATA_DIRS, just wrap the
firefox binary directly and adjust PATH. The former did not work with
Phosh, and on second thought, wrapping the binary is what's really
necessary. The launcher would have been just another useless layer.