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I don't recognize your assumptions as Scriptural. Instead I find in the Bible that man is incapable of doing anything righteous, and that true faith, once given, is non-refundable because it's predicated on God's plan for His creation. It's His call.

Either we have been redeemed by Christ's atonement alone or we haven't.

"And with all deceivableness of unrighteousness in them that perish; because they received not the love of the truth, that they might be saved.
And for this cause God shall send them strong delusion, that they should believe a lie:
That they all might be damned who believed not the truth, but had pleasure in unrighteousness.
But we are bound to give thanks alway to God for you, brethren beloved of the Lord, because God hath from the beginning chosen you to salvation through sanctification of the Spirit and belief of the truth " -- 2 Thessalonians 2:10-13

"Chosen to believe."

"Chosen to believe."

Where does it say that?

It says that there are those who do not believe because they have not the love of the truth.

For those who do believe, God has chosen them for salvation (election) through sanctification (Eph.1).

God knew who would believe and who would not and chose those who would to be saved in Christ (New Testament).

All men were savable and all had a choice to respond or reject God's free offer of salvation.

This verse lines up with Rom. 8 and Predestination to ultimate glorification being conformed to the image of Christ.