Firstly, I believe that God provides a preaching of the gospel prior to regeneration.
If you want to compare it to building a fire, he causes the firewood to be laid down first, prior to regeneration, which causes the woodpile to explode into flames.
The difference between Reformed and free-willer theology is that they believe they cause the woodpile to explode into flames by their faith and repentance, which they provide. The Reformed position would be that God causes the woodpile to explode into flames, and faith and repentance results.
And, in regards to the "broader context of Scripture", free willers DO NOT acknowledge that God CHOOSES individuals for salvation, because in their mind it is unfair. Well, the fair thing is that everyone goes to eternal punishment, and that none are saved.
The Reformed view is that God elects a certain group of individuals, who are given to the Son. The Son redeemed this group from their sins, and it was an ACTUAL and PERSONAL redemption. The Holy Spirit applies this redemption to this group in time.
This is clearly taught in Scripture, and is the grander context of salvation.
I have laid out, specifically, the Scriptures that refer to this on other threads, but there is a book called Five Points of Calvinism by David Steele which also lays this out very well.
It is no less fair for God to choose certain individuals for salvation, than for him to select certain individuals for salvation at the time of Noah, and to let the rest drown.
That may not appeal with some folks' Play-doh, free-willer view of God, but if it is what Scripture teaches, we cannot argue with it. Ad it definitely teaches that GOD CHOOSES, and not based on individual merit.
John 6, 8,10, Ephesians 1, 2, Romans 8-11, 1 Cor 1:26ff would be good places to start in this regard.
It is plain that certain individuals have been given to the Son, and others are not.