How can I reconcile the idea of liking myself (in order for others to like me) with the virtue of humility and the subsequent entailing necessity of despising myself and my sinful acts, the product of my imperfect nature?
Humility has already been addressed a lot on the Question and Answer Link of the Southern Diocese Website regarding humility. I encourage you to review these specific questions and answers on this subject.
The idea of liking yourself means to be reconciled with yourself, not in a prideful way; simply because you are the temple of God and the Holy Spirit abides in you.
Further, I would like to to introduce you to the attitude of seriousness. Our attitude of seriousness reflects the way we view life; and how seriously we take it. Seriousness means to acknowledge the value of your own life, how precious it is in God's Holy eyes and in others. The Lord said, "For what a man profited if he gains the whole world and loses his own soul?" (Matthew 16:26). You are a person whom God is interested in and has a special plan for.
St Paul said, "But when it pleased God, who separated me from my mother's womb and called me through His grace, to reveal His Son in me" (Galatians 1:15-16).
Seriousness dictates me to humbly trust in God. God created me, chose me as His child, and will grant me success. He has a special plan for me; I will never fail, be depressed or upset.
We know St. Athanasius spent most of his life in trouble and humbly rejoiced even during his darkest times because he felt that the Lord Jesus Christ was with him.
In conclusion, with humility AND seriousness we give thanks to the Lord and praise His Holy Name.