How can a young man reconcile his desire to marry a girl he deems suitable for his religion and life with his father's refusal of this marriage, knowing that the girl has refused to marry anyone else and has helped him in his life?

The woman and her mother did well in advising you that a father cannot be replaced. Try to convince your father through an intermediary whom he respects. If he agrees, then all is well. Otherwise, look for someone else, in obedience to him. Engagement is merely a promise, and perhaps Allah intended good for you. If you have committed a sin with her, then repent to Allah, for relationships outside the framework of marriage are forbidden.