What I said was that God is capable of being sovereign without those acts in a universe of free wills. Calvinism says otherwise.
I'm not sure what you are stating here. I'm sure we'd both agree that God is sovereign and is always sovereign over His creation. And from your statement we both agree that God interacts with men. The real question is whether man has the God-given ability to stop God's purpose or not? There are really only two scenarios in answer to this question:
Scenario #1-Arminian View
If it is God's intention to save everyone equally, then God has given every man everywhere the same rights and abilities to make a rational choice. If man so chooses at some point in time and just say no to the gospel, then is that's the end of it? Does God just say, "Well, that's that." and walk away? In the matter of salvation, God doesn't give up His sovereignty but He doesn't exercise any extra divine will to help an individual to see the truth. That would be unfair. Every man has the same God-given right to say that he wants to go to heaven or hell, and the same level of activity is equally applied to everyone.
Of course, there are exceptions to this salvation rule depending on how young a person might be or how infirm. Those are special cases that God handles on a case by case basis. Then there are the cases where God directly calls an individual like John the Baptist or Paul. Those are unique. But the bottom line is that there is no need to pray for the salvation of someone's soul simply because they are already afforded the same "free will" to make their choice that everyone else has.
As far as works, man has been given instructions and is free to carry out those orders. Works rest entirely with the free will of man to be obedient to doing "the things of God". God may or may not intervene in the process. If man rejects being obedient, then he is certainly poorer for it and loses his rewards. But God just changes His plan to effect His outcome without an individual's help. Man may experience indirect chastisement by not being in God's will, but there's no need for God's direct chastisement because this is man's free will.
Depending on how much you buy into this view, man is capable at any time of saying they have had enough and leave the fold. That is what free choice is all about. One persumes that you don't lose your free will when you become a Christian. But, they could by their own choice, lose their salvation.
Scenario #2-Reformed View
In the Reformed scenario, man is hopelessly trapped in sin. He can't do anything to rescue himself. But worst, he is bent to do those things that are opposed to God, either overtly or covertly.
God understands man's predicament and exercises His grace and mercy to turn individuals to Himself. This is not an easy process from a worldly perspective. But nothing too difficult for our God. It requires God giving us knowledge of the truth, bringing us to repentance, changing our hearts, giving us the faith to cry out to Him.
Even after salvation, we continue to rebel but true believers hearts are soften and are more responsive to God. God is patient and loving, even giving us His Spirit to slowly work in our hearts to perfect us. He's not in any hurry.
This change of heart makes us more willing to do His will. The fruit of our labors are sprinkled along our sanctification path handed out by God, even though we may not see them. We simply rest in His promise that we will bear fruit*. If we go astray, God prods us back into place with His rod and staff to do His will like a loving father guiding his son. Those who know the Father don't mind being chastised because it perfects them in knowing what they've done wrong. We learn by the fruit God gives us and the chastisements we experience. Everything works together for our good.
To those who are called, we will never lose our salvation because God will not allow it. He has spent too much time working and nuturing us to allow it to happen. We will never stray too far off that path that God will not guide us back.
It remains unclear why God has chosen some and not others. Those who are called pray that God would grant other people the same ability to have their eyes opened. It is possible that God has planned to honor those prayers by granting the eyes and ears of others to be opened. This again may be one of those fruit of our labor sprinkled along our paths. But whether or not God will honor our prayers for the direct intervention of salvation of others, we know that God is sovereign and knows what He's doing.
Everyone justly deserves hell. What is difficult to explain is mercy.
*It is my view (not Reformed), when we get to heaven we will all throw down our crowns at our Lord's feet because He did it all.