I'm not sure if I'm blowing your mind here mate but total precision/objectivity on position cannot possibly exist. It's a fiction. You may as well invent a dragon monitoring machine. It cannot do the job you're asking of it.
So you do what ever other person who deals with precision does, and accept objective total precision can't exist and introduce tolerances. Those tolerances should be "clear air" rather than "millimetres" because the latter provides no clear advantage to the player, which is the point of the offside rule, and the former does.