Firefox couldn't do the link thing itself without either being a setuid binary, or running somewhere the user could replace Firefox. You could MAYBE get it to make a symlink under XDG_RUNTIME_DIR, or /tmp if that's unset, since symlinks work across devices. At least on my desktop /tmp is allowed to contain executables and a symlink to /usr/bin/bash executes and remains named as the symlink path.

Though it'd still be many times better if Firefox made it easier to tell which profile was associated with a given process (prefix the argument list as if launched with that). ALSO if KDE's task list supported improved flexibility for group categorization. It wouldn't even need to run an external program other than once for each new window created.