You're claiming that salvation is attained by man and God cooperating together to achieve salvation. The problem with that idea is the Lord Jesus said in, John 3:3, a person must be "born again" (regenerated) by the Holy Spirit just to see or desire the Kingdom of God.
The Fall affected every part of human nature, including the mind, heart, and will. While unbelievers can make everyday choices, they lack the spiritual desire or "moral ability" to choose God.
1 Corinthians 2:14, which states that the natural person cannot understand the things of the Spirit because they are "folly to him".
Because faith is a gift and humans are spiritually dead, salvation is entirely a work of God from start to finish. God must first sovereignly change the sinner's heart so that they want to believe the gospel.
As Jesus said, "Seeing they do not see, and hearing they do not hear, nor do they understand" (Matthew 13:13). Paul explains that the problem is not lack of information but lack of spiritual discernment. The gospel seems like foolishness to the natural man because he does not have the Holy Spirit.
The sinner’s condition is not like a man who wants to believe but cannot. It is more like someone who hates the offer and wants nothing to do with it. "You refuse to come to Me, that you may have life" (John 5:40). Why? "Because the light has come into the world, and people loved the darkness rather than the light, because their deeds were evil" (John 3:19).
It's correct that we are called to God to be His people. He will call whom He pleases...
We are then to out our faith in Jesus to abide with Him and be saved. Faith is not works and doesn't remove from His sacrifice in any way. We are to put our faith in Him (Mark 16:16) and not fall away (Hebrews 6:4-6).
If we are God's people, we are to remain so. Works then will stem from this lige with Jesus if we love Him and believe in Him.