Man's will doesn't diminish God's sovereignty at all - it confirms it.
If man didn't have a will, then God doesn't have a will either - because man was made in God's image.
But since man has a will, it is confirmed that God has a will - since man was made in God's image.
God is holy, and we are commanded to be holy as He is holy - and He has appointed a day of judgment. The necessity for judgment confirms that man has a will. If the only will that existed was God's will, then there should be no necessity for judgment - for God can't judge Himself!
The fact that I own freehold title to my land diminishes nothing of the Crown's sovereignty - it confirms it.
Crown sovereignty is the source of my freehold title. Crown sovereignty sets the limits of my title. Even though I have title, I'm still subject to judgment by the Crown if I break laws on my own land.
Similarly, anything that God sovereignly decides to do, confirms His sovereignty, rather than denies it.
Since God sovereignly decided to make man in His own image, and gave man a will, then the fact that man has a will is evidence of the sovereign action of God who gave man a will in the first place.
Seeing man is sovereignly given a will, it follows that man is also subject to sovereign, divine law - and to judgment.
It's appropriate for a father to tell his child who lives in his house, what to do. But when the child is grown, married and lives in his own house, the father now knocks on his son's door before entering. He is still his father - but his son has his own house now.
God created sons to be mature sons - not undeveloped children. He delights when we use our will with the same ethics with which He uses His.
Marriage is an example of God sovereignly subjecting Himself to the limitations of a subsequent principle - without diminishing anything of His sovereignty. When a man and woman decide to get married, God puts them together - and forever thereafter God relates to the couple as one, respecting the decision the couple made to get married.
God remains sovereign over both individuals, yet He no longer treats them as though they were not a couple. In all His actions towards the couple, He is now duty-bound to regard them no longer as individuals alone but also as a couple.
After they were married, the sovereign God now frames His own actions towards the couple by the terms of a subsequent law - the law of marriage.
The fact that God's regard for the couple must now be framed by the fact that the couple had decided to get married, takes nothing away from the sovereignty of God - it confirms His sovereignty, because it was God who sovereignly decided to create the law of marriage in the first place.
Their decision to marry forever shapes the way God sees them - yet within the provisions of that framework, the couple remains subject to sovereign, divine law.
Similarly, God's sovereign decision to make man in His own image, giving him a will, takes nothing away from His sovereignty, but confirms it. Man's will can affect the way God relates to man - and yet it is still subject to sovereign, divine law and judgment.
Man's will has limitations though - it can't achieve as much as God's. Man is subject to time and death - but God can predict man's choices and He can control certain political destinies spanning generations - not by removing man's will, but by working with it, by keeping someone alive or not - as He did with Pharaoh, and as He did with the unbelieving nation of Israel. He didn't remove their will, but He kept them alive for His own time and purposes.
Pharaoh was like a cleaner-fish in an aquarium. A cleaner fish does what it does by nature - it goes along cleaning up the mess from the other fish in the aquarium. It goes along happily doing what it does, unaware that it is fulfilling someone else's purpose - its owner's purpose.
Similarly Pharaoh was doing his own will, unaware that God, who could have judged him earlier, instead allowed him to rise to a prominent position for His own purpose (so that God's judgment and deliverance would be public).
God couldn't have judged Pharaoh if Pharaoh hadn't had a will of his own. Pharaoh had a will of his own, and was therefore subject to Sovereign judgment - yet God still worked-out His purpose in history by delaying Pharaoh's judgment and allowing him to rise to prominence for such a time.
In the same way, natural Israel was allowed to exist, despite its self-will and unbelief - so that God's judgment and the salvation of believers could both be demonstrated. That's what Romans 9 is about.
Indeed God's salvation plan did not originate with a man's will or running - but with God Himself. He sovereignly offered salvation upon His own sovereign basis - faith. Man's will and running had nothing to do with deciding that basis - God Himself decided it. And faith to live by is not a work: it's a gift for all to receive. Receiving a gift is not a work. The door of faith is open. Whosoever will may come.
Everything in life is a gift. Faith is a gift - and it is offered to all. Therefore if some don't have faith, it's not neccessarily because God hadn't offered it to them - some simply may not have liked to take advantage of the offer. Yet even this is within God's sovereign allowance.
I feel that I'm taking Scriptures on face value, in context, comparing Scripture with Scripture, and without manipulation.