The terms "monergism" and "synergism" ain't in the Bible. The Bible is an invitation to man, he has the free-will choice to either accept or reject. (Isa. 45:22; Jn. 3:19; Rev. 22:17). Frame it as the Bible does or not at all. God does not save by fiat. That's what monergism means.
The concept of "free will" is not found in the bible. So your argument is self defeating. We affirm that the gospel is to be proclaimed indiscriminately to all people. God does not hold anyone back from believing. Their rejection of Christ is because men love darkness, hate the light and will not come into the light (john 3:19). To claim man has a free will assumes the unbiblical idea that fallen man is willing to come to Christ apart from the Holy Spirit. But no one can say Jesus is Lord apart from the Holy Spirit (1 Cor 12:3) so we cannot ascribe our faith and repentance (even partly) to our own humility, wisdom, good intentions, or sound judgment but to grace.
Jesus declared, "the Spirit quickens, the flesh counts for nothing...that is why I told you that no one can come to me unless the Father who sent me grants it" John 6:63, 65
And if no one comes to faith in Christ unless God grants it then no one by their natural free will ever comes to him.
The Apostle Paul said, "we preach Christ crucified, a stumbling block to Jews and folly to Gentiles, but to those who are called, both Jews and Greeks, Christ the power of God and the wisdom of God." 1 Cor 1:23-24
The call of the gospel is universal but, according to Paul, all men reject it (folly, stumbling block) but to those among them who are called by God, the power and wisdom of God.
Monergism does not mean people are saved simply because they are elect. Election by itself saves no one. People are saved by the gospel of Jesus Christ. We cast the seed of the gospel indiscriminately but only God can take it from their ears to their heart. Only God can disarm mens hostility, open their blind eyes, unplug their deaf ears and turn their heart of stone to a heart of flesh. That is called mercy.
You teach that salvation depends on human will, but the Bible teaches (and I quote) 'it depends not on human will or exertion, but on God, who has mercy." (Rom 9:16)
Yes we all agree that God commands us to trust in the gospel of Jesus Christ. But a command does not presuppose a willingness on our part. That is something you are adding to the scripture that simply isn't there. So the concept of monergism (salvation by grace alone) is there clearly taught in the scripture, but free will isn't anywhere to be found. We do indeed have a will ... and TO WILL is something we all do naturally, but to will ARIGHT is by grace, and grace alone.
Note: the word "monergism" is from "mono" which means "one" and "ergon" which means "work". In other words, salvation is of the Lord... it is His work, not ours. Nothing could be more biblical.