Free will means all people have partial salvation.
Partial? No offense but this has not only no scriptural basis, it doesn't make logical sense. Jesus taught that there were two possibilities for us on the 'Last Day' or day of Judgement.
1. Live in paradise with Jesus.
2. Be cast into the lake of fire.
There is no in between option. There is no such thing as partial salvation.
Whether or not you have free will has no bearing on this according to what Jesus laid out. You've started off with a false premise and thus the rest of the line of your conclusions can't be drawn. The starting point is already in error.
But it always results in people trusting in themselves for salvation. God only opening heaven’s doors to those who complete the task.
Ephesians pretty much destroys this idea. The works that God prepared for us (from before the foundation of the world) to walk in were his, not ours. The works we do in response to God's calling is "not of yourselves." That doesn't mean we are not doing the work, it means we can't invent any work that would save us. Thus, what we have to do is trust that he delivered all of the information required that we might be saved.
When Cornelius spoke first to Peter, he was expecting "words," because that is what the angel told him. It was also what Peter was commanded to deliver. And what he did then was to go and deliver those words, at which point Cornelius obeyed with his household.
But this destroys faith in Christ as savior. Free will is a walk by sight trust in yourself for salvation based on rules you fulfill. So trust is always in self who fulfills them.
Free will is merely the ability to freely make choices without any coercion. It is self-evident that we have free will and can chose to believe. Were this not the case, then God wouldn't have delivered commands to anyone. He would have merely made them do his bidding. I don't think anyone doubts that he has the power to do that.
But without free will, people have to look for a power beyond themselves to save. Only when they come to the end of themselves with nothing more they can do, will Christ become their only focus of faith.
Even with free will, we would have no power to save ourselves. Free will does not negate the power of God. It is proof of the power of God.
As Martin Luther said; "First, God has promised certainly His grace to the humbled: that is, to the self-deploring and despairing. But a man cannot be thoroughly humbled, until he comes to know that his salvation is utterly beyond his own powers, counsel, endeavours, will, and works, and absolutely depending on the will, counsel, pleasure, and work of another, that is, of God only.”
Luther would be here refuting himself when he uses the words "self-deploring and despairing", if in fact this is his evidence for a lack of free will. But I am not sure this is what he is doing. He asserts that a person's humility is from his own conscience and not coercion. A person could only humble
himself if he has a free mind with which to come by that determination. If he hasn't a free mind, then there is some external cause for this humility which would then negate the idea that he humbles himself. If an external force has humbled him, he isn't humbled at all, he is forced into submission.
He continues; “For if, as long as he has any persuasion that he can do even the least thing himself towards his own salvation, he retain a confidence in himself and does not utterly despair in himself, so long he is not humbled before God; but he proposes to himself some place, some time, or some work, whereby he may at length attain unto salvation. But he who hesitates not to depend wholly upon the good-will of God, he totally despairs in himself, chooses nothing for himself, but waits for God to work in him; and such an one, is the nearest unto grace, that he might be saved." Martin Luther. The Bondage of the Will.
There is a difference between obeying a command from God which results in one's salvation, and thinking that one can invent his own criteria. Personally, I think Luther is right here. I think it is the modern day reader who misuses these words to claim it is proof of any lack of free will. You can be humble, realizing that you are not the author of your own salvation, and still do what is required to achieve that salvation which you had no power to accomplish. The distinction has to be made between what a man can do and what God can do. Man couldn't provide a sacrifice good enough to achieve remission of sins for the whole world. But he can obey the commands which are said to accomplish this remission in himself. In fact Ephesians 2:10 says that it is exactly why God created us.
So in the end people have sight faith, trusting in tangible items keen to the senses. But only few have faith sight where they trust in Christ alone to save them.
God
gave us the tangible things. He made sure they were written down because he wanted us to have the knowledge. Having that knowledge does not destroy faith, it is the very
basis of our faith. One cannot believe anything in particular without first getting the information as to what that belief entails. Believing what God told us IS ITSELF FAITH. It isn't negated by any doctrine of man.
I'm convinced that Jesus preached free will. What does he ask of us?
Luke 14:28
"And whoever does not carry his cross and follow Me cannot be My disciple. 28 Which of you, wishing to build a tower, does not first sit down and count the cost to see if he has the resources to complete it? 29 Otherwise, if he lays the foundation and is unable to finish the work, everyone who sees it will ridicule him,…"
Whose cross is being carried here and who is it that is expected to carry it to the end? God? Who is it that is told he must consider everything involved? If Jesus EVER taught that God was going to carry
your cross for you, I haven't seen it. Jesus clearly shows us that we have our own crosses we must carry. So it's a joint endeavor which is of course not possible without him. But it doesn't ONLY involve him as even Martin Luther points out.
I think that Luther was correct in what you've quoted. I just don't think it means what you are saying it means and what many modern readers think.