I think your post was well written and I agree in large part with it. Allow me to offer further evidence towards the notion that Paul was neither Calvinistic or Armenianistic, but both of these doctrinal systems ignore the truth.
I think both Calvin and Arminius were wrong because they both made the same fatally flawed assumption; they both assumed that salvation was a direct result of faith. Neither of them realized that this was only true for Abraham, and that the rest of us are saved by our faith in the gospel of Jesus Christ qualifying us as an adopted descendant of Abraham and therefore an heir of Christ's righteousness which was exchanged 1:1 between Jesus and Abraham.
If salvation were direct, then our faith would cause regeneration. However, salvation is indirect because our faith causes
human adoption. Christ’s righteousness was exchanged with Abraham, then, as sons of Abraham, the second step is we
inherit Christ's righteousness according to God’s promise to Abraham that his seed would inherit the righteousness. Therefore, we see salvation is indirect. Human adoption doesn't require regeneration. In fact, God commands us to make the choice of salvation, and God says it is a choice every human being is capable of making. This command is given three times in Deuteronomy 30, and each time God re-iterates that it is a human choice – a choice set before us. Moreover, God states unequivocally that it is a human choice, and not a choice made in heaven in verses 11-12.
Deuteronomy 30:1
So it shall be when all of these things have come upon you, the blessing and the curse which I have set before you, and you call them to mind in all nations where the LORD your God has banished you,
Deuteronomy 30:6
Moreover the LORD your God will circumcise your heart and the heart of your descendants, to love the LORD your God with all your heart and with all your soul, so that you may live.
Deuteronomy 30:11
For this commandment which I command you today is not too difficult for you, nor is it out of reach.
12 It is not in heaven, that you should say, 'Who will go up to heaven for us to get it for us and make us hear it, that we may observe it?
Deuteronomy 30:15
See, I have set before you today life and prosperity, and death and adversity;
Deuteronomy 30:19
I call heaven and earth to witness against you today, that I have set before you life and death, the blessing and the curse. So choose life in order that you may live, you and your descendants,
This human choice comes before regeneration. I don’t think completely free will is Biblical. I think it’s clear that, as it pertains to Salvation, God gives human beings a distinct, binary choice. Choose life or choose death. It does nothing to damage the sovereignty of God to command humans to choose between two options. For example, if I told my child “you can have pancakes or oatmeal for breakfast… but FYI, the pancakes are awesome,” I don’t lose my sovereignty over breakfast. My child cannot, for example, choose steak and eggs. So who determines breakfast – me or my child? I would say I have determined breakfast, and not my child because I have the ingredients for only those two choices. However, so has my child played a role. So who determines salvation – man or God? Yes! Man and God both play a role, but ultimately, we cannot make choices outside of the limited scope God gives us.
Joshua 24:22
Joshua said to the people, “You are witnesses against yourselves that you have chosen for yourselves the LORD, to serve Him.” And they said, “We are witnesses.”
Romans 8:16
The Spirit Himself testifies with our spirit that we are children of God,
17 and if children, heirs also, heirs of God and fellow heirs with Christ, if indeed we suffer with Him so that we may also be glorified with Him.
Deuteronomy 19:15
A single witness shall not rise up against a man on account of any iniquity or any sin which he has committed; on the evidence of two or three witnesses, a matter shall be confirmed.
As Romans 8:16-17 shows, both God’s spirit and our own spirit must play a role in salvation, just as Deuteronomy 30:19 says God calls heaven and earth as co-witnesses of the choice we make for salvation. One last point I’ll make about Total Depravity is that the Bible says The Law is good. The Bible also says that God has written His law on our hearts, and on the hearts of unbelievers, so that all are without excuse. We cannot be completely and entirely depraved if we have God’s good law written on our hearts so that we know the difference between good and evil. In fact, the very first sin was partaking of the tree of the knowledge of good and evil.
Romans 2:14
For when Gentiles who do not have the Law do instinctively the things of the Law, these, not having the Law, are a law to themselves,
15 in that they show the work of the Law written in their hearts, their conscience bearing witness and their thoughts alternately accusing or else defending them,
So I agree that neither Calvinism nor the teachings of Jacobus Arminius are accurate. This is probably why the argument between the two sides has perpetuated without end for so long, being unresolvable because both are fundamentally wrong about how salvation works.