I guess a command line parameter might be possible, although as far as I know it is not so easy to read custom command line parameters in a standalone Unity build. Think a plugin might be needed, and, it may not work equally on all operating systems. So, it's not a path I would want to go unless it's absolutely necessary.
Since I use Unity for development I do not have direct access to the input, I use Unity's input manager. So, if it is correct as I read on another forum (that there is some kind of bug in Unity's joystick input on Linux) there might not be so much I can do about it myself. It would in that case be something that the Unity team would need to look into.
Hope the stored calibration values can be useful as a possible work-around.