I have read Calvin's commentaries on John, 1 John, and 1 Corinthians, and have found nothing that actually contradicts Scripture. He examines the available interpretations, says what he rejects, what he can live with, and what he prefers. In terms of Election and Predestination, he examines the relevant Scriptures and gives what he sees in them. He accepts that the way these work is essentially a mystery, and accepts that if the Scripture says that we are elected and predestined before the foundation of the world, we have to accept it in faith and not let them get in the way of giving the invitation to all to receive and believe the Gospel.
It seems that many who are dogmatic about "Calvinism" have come to their own conclusions without giving Calvin himself a comprehensive reading. I have come to the conclusion that a lot of dogma around Calvinism and the opposition to it is based on presumption rather than a fair balance between what God has revealed to us in Scripture and what remains mystery that God has chosen not to reveal to us. A lot of it is trying to second-guess God in areas where He has not made things clear in Scripture. God has not chosen to reveal the inner workings of Election and Predestination. He just says that they just are and we have to take His word for it for now.
The problem is that we have those who are over-curious about the ways of God and require hard and fast answers to everything that God does, even in areas where He has not revealed to us. What we have in Scripture is sufficient for people to believe in Christ and be saved. The Bible is a book about Christ and we should see it in that light. It is not a comprehensive scientific, history, or the nature and character of God.
When Jesus went through the Scriptures with the two disciples at Emmaeus, He didn't delve into the inner workings of God. He showed them, from the Scriptures, all about Himself. They didn't need to know whether they were elected or predestined. All they needed to know was that God's plan of salvation involved no one else but Jesus, and that faith in Him is the only way to eternal life.