Averagefellar, you asked, “How does man overcome his depravity?”

Man cannot. God does it for him.

You said, “Because a choice is presented does not necessitate that one be in any type of state, specifically; not perfect, fallen or equipoise.”

It depends on what kind of choice it is. The Bible distinguishes between willful sins and unintentional sins, for example. F.F. Bruce, Rylands Professor of Biblical Criticism and Exegesis at the University of Manchester, England, and editor of The Evangelical Quarterly, commented on Hebrews 10:26-29:

“But the writer to the Hebrews himself distinguishes (as did the Old Testament law) between inadvertent sin and wilful sin, and the context here shows plainly that the wilful sin which he has in mind is deliberate apostasy. People who commit this sin, he says, cannot be brought back to repentance; by renouncing Christ they put themselves in the position of those who, deliberately refusing His claim to be the Son of God, had Him crucified and exposed to public shame. Those who repudiate the salvation procured by Christ will find none anywhere else.”
(Bruce, “The Epistle to the Hebrews,” The New International Commentary on the New Testament, page 124)

The Bible makes it clear that sins of ignorance (unintentional sins) can be forgiven. Notice the following passages:

Now when these things have been thus prepared, the priests are continually
entering the outer tabernacle, performing the divine worship, but into the
second only the high priest enters, once a year, not without taking blood,
which he offers for himself and for the sins of the people committed in
ignorance. (Hebrews 9:6-7)

And the priest shall make atonement before the LORD for the person who
goes astray when he sins unintentionally, making atonement for him that
he may be forgiven. (Numbers 15:28)

The apostle Paul said that even his blasphemy as a non-Christian could be forgiven because he “acted ignorantly in unbelief” (1 Timothy 1:13). He was not experiencing the special, illuminating, irresistible conviction of the Holy Spirit when he blasphemed. When Paul unintentionally sinned as a Christian, he said that he was not doing “what I would like to do” (Romans 7:15); rather, “sin which dwells in me” was responsible for his actions (Romans 7:17).

When Peter addressed the Jews in Jerusalem after the crucifixion of Jesus, he said that they “acted in ignorance” (Acts 3:17) when they put Him to death. Jesus said from the cross, “Father, forgive them; for they do not know what they are doing” (Luke 23:34).

Willful (defiant, intentional) sin, however, is an unforgivable type of blasphemy. Again, notice the following passages:

But the person who does anything defiantly, whether he is native or an
alien, that one is blaspheming the LORD; and that person shall be cut off
from among his people. Because he has despised the word of the LORD
and has broken His commandment, that person shall be completely cut off;
his guilt shall be on him. (Numbers 15:30-31)

“Therefore I say to you, any sin and blasphemy shall be forgiven men, but
blasphemy against the Spirit shall not be forgiven.” (Matthew 12:31)