I know what Reformed people (Calvinists) believe. They believe people are incapable of believing the Gospel unless God intervenes in their life. IOW, God has to give a person the ability to believe in God before that person can believe. I do not agree.
The gift of God in Eph 2:8 is not the faith to believe, it is salvation BY faith.
The gift of God in Ephesians 2:1-10 is the entire package, including the faith, and there is no reason to boast.
You are correct that Reformed individuals believe that God gives the person a heart of flesh, to replace the heart of stone, and it is this heart of flesh which produces the faith and repentance. God does not expect a dead heart of stone to produce faith and repentance. He needs to spiritually resurrect the person before they can produce this faith and repentance. This is called regeneration, or being made alive again.
I suggest that those who are willing to hear would read Ephesians 2:1-10 carefully.
In Reformed theology, there is no reason for anyone to boast whatsoever in their salvation, because God gave them the heart of flesh that enabled the response.
In free-willer theology, the person can boast over his faith and repentance, because he dredged faith and repentance up from his stony heart. Their view is that their effort in this regards leads to their regeneration, or being born again.
They really do not take seriously what Scripture teaches about the unredeemed state of mankind. They claim man is not spiritually dead, but he retains the ability to pull himself up and grasp salvation. So, at the very least, they can boast that they were smart enough or whatever to take advantage of the opportunity for salvation.
Like I said, it's a totally different way of thinking. Even Arminius didn't believe what current day free-willers believe. He was smart enough to know that mankind could not choose God without an act of grace on his behalf.
Arminius also did not believe what the Remonstrants taught, who later came to be called Arminians. Like I said, he was not so berift of biblical understanding that he would believe what free willers believe today.