Am I to consider my wife a stranger to me after the third divorce due to her repeated departures without my permission?

As long as you have divorced her with the third pronouncement, she has become irrevocably separated from you, and she is forbidden to you, based on the words of the Almighty: "And if he has divorced her (for the third time), then she is not lawful to him afterward until she marries another husband." The reason for the divorce is not considered; what is considered is the husband's pronouncement of it, and you have pronounced it three times. Thus, your wife has become a stranger to you.