What should I do to feel at ease after my shortcomings in honoring my deceased father, even though he knew of his satisfaction with me before his death?

If avoiding the father is out of fear of harm or disobedience, then there is no blame in that. The father's contentment is from Allah's contentment. It is recommended to supplicate for the father, seek forgiveness for him, and give charity on his behalf after his death, and to honor his loved ones, maintain ties with his kin, and pay off his debts.