Is there a common theme ?

That is OK. We all need to come to that point. It is only then that we can begin to build upon the bedrock of truth. Welcome to the light.

Thus saith the TULIP. Now lets read the Bible...

Romans
1:19 Because that which may be known of God is manifest in them; for God hath shewed [it] unto them.
1:20 For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, [even] his eternal power and Godhead; so that they are without excuse:
1:21 Because that, when they knew God, they glorified [him] not as God, neither were thankful; but became vain in their imaginations, and their foolish heart was darkened.
1:22 Professing themselves to be wise, they became fools,
1:23 And changed the glory of the uncorruptible God into an image made like to corruptible man, and to birds, and fourfooted beasts, and creeping things.
1:24 Wherefore God also gave them up to uncleanness through the lusts of their own hearts, to dishonour their own bodies between themselves:
1:25 Who changed the truth of God into a lie, and worshipped and served the creature more than the Creator, who is blessed for ever. Amen.

Yeah - especially when it is done by someone who says this.

Your illustration above defies itself - particularly in the clash between "born -physical birth" and "appoint oneself as a child of God" -- which is it - physical birth or spiritual birth? (And the answer is: 'spiritual birth')

John 1:

12 But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name: 13 Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.

You seem to be confusing what verse 12 is saying with what verse 13 is saying.

Look up the definitions of the word 'received' in verse 11 and verse 12. You should notice that they are different.

And, you can see why if you look carefully at the context of each verse.

Now look closely at the definition for the word 'received' in verse 12. This is an action on the part of the one doing the receiving.

In this context, according to this definition, one cannot receive [anything] without one's own will coming into play.

In verse 13, the word 'born' is referring to the spiritual rebirth of individuals - which is of God with no effect from man.

Verse 12 is about the will of individuals - believing in/on God/Jesus. Verse 13 is about the rebirth being 100% all God.

Amen! Nothing difficult here, or anywhere else in the Bible. Error and misunderstanding is what is difficult.

These scriptures has reference to the regenerated, not to the natural man, that cannot hold the truth in unrighteousness if he has never held the truth, which contains the things of the Spirit. 1 Cor 2:14.

True. All true. Oh - EXCEPT for one thing...

It is by the power of God - through and by the Word of God - that the natural man is given the ability to choose something outside of his own nature.

It is that simple.

Hebrews 4:

12 For the word of God is quick, and powerful, and sharper than any twoedged sword, piercing even to the dividing asunder of soul and spirit, and of the joints and marrow, and is a discerner of the thoughts and intents of the heart.

Heb 4 verse 7 says "if you will hear his voice". John 10:27 My sheep (regenerated children of God) hear my voice. The natural man that has not been regenerated can not hear his voice.

Let me get this straight. Are you saying that the natural man, as described in 1 Cor 2:14, received the spiritual things that Jesus taught?

When was Peter born again ? Jesus taught Peter the ' spiritual things of his death burial and resurrection after teaching him and the deciples for years . They did not understand the Gospel let alone most of what he said .
Luke 18
31¶Then he took unto him the twelve , and said unto them, Behold, we go up to Jerusalem, and all things that are written by the prophets concerning the Son of man shall be accomplished.
32For he shall be delivered unto the Gentiles, and shall be mocked, and spitefully entreated, and spitted on:
33And they shall scourge him, and put him to death: and the third day he shall rise again.
34¶And they understood none of these things: and this saying was hid from them, neither knew they the things which were spoken .

1 cor 2 v 6

6¶Howbeit we speak wisdom among them that are perfect( full grown ) : yet not the wisdom of this world, nor of the princes of this world, that come to nought:

13¶Which things also we speak, not in the words which man's wisdom teacheth, but which the Holy Ghost teacheth; comparing spiritual things with spiritual.
14But the natural man receiveth not the things of the Spirit of God: for they are foolishness unto him: neither can he know them, because they are spiritually discerned.
15But he that is spiritual judgeth all things, yet he himself is judged of no man.

1¶And I, brethren, could not speak unto you as unto spiritual, but as unto carnal, even as unto babes in Christ.
2I have fed you with milk, and not with meat: for hitherto ye were not able to bear it, neither yet now are ye able.

This is the problem with a system that dictates what the bible has to mean . Thats essentially what you've just said there. You think your ' harmonising ' ,but What your actually doing is this ," well I know regeneration preceding faith ' must be true , so therefore when it says they hold the truth , well hmm this must really be a born again believer, because only regenerated people hold truth " Rather than seeing the obvious fact that it is Paul describing man's general condition after the fall . That no one can attain through their own righteousness eternal life . They hold the truth in unrighteous rather than acknowledge and come to God .

When was Peter born again ? Jesus taught Peter the ' spiritual things of his death burial and resurrection after teaching him and the deciples for years . They did not understand the Gospel let alone most of what he said .
Luke 18
31¶Then he took unto him the twelve , and said unto them, Behold, we go up to Jerusalem, and all things that are written by the prophets concerning the Son of man shall be accomplished.
32For he shall be delivered unto the Gentiles, and shall be mocked, and spitefully entreated, and spitted on:
33And they shall scourge him, and put him to death: and the third day he shall rise again.
34¶And they understood none of these things: and this saying was hid from them, neither knew they the things which were spoken .

1 cor 2 v 6

6¶Howbeit we speak wisdom among them that are perfect( full grown ) : yet not the wisdom of this world, nor of the princes of this world, that come to nought:

13¶Which things also we speak, not in the words which man's wisdom teacheth, but which the Holy Ghost teacheth; comparing spiritual things with spiritual.
14But the natural man receiveth not the things of the Spirit of God: for they are foolishness unto him: neither can he know them, because they are spiritually discerned.
15But he that is spiritual judgeth all things, yet he himself is judged of no man.

1¶And I, brethren, could not speak unto you as unto spiritual, but as unto carnal, even as unto babes in Christ.
2I have fed you with milk, and not with meat: for hitherto ye were not able to bear it, neither yet now are ye able.

When was Peter born again ? Jesus taught Peter the ' spiritual things of his death burial and resurrection after teaching him and the deciples for years . They did not understand the Gospel let alone most of what he said .
Luke 18
31¶Then he took unto him the twelve , and said unto them, Behold, we go up to Jerusalem, and all things that are written by the prophets concerning the Son of man shall be accomplished.
32For he shall be delivered unto the Gentiles, and shall be mocked, and spitefully entreated, and spitted on:
33And they shall scourge him, and put him to death: and the third day he shall rise again.
34¶And they understood none of these things: and this saying was hid from them, neither knew they the things which were spoken .

1 cor 2 v 6

6¶Howbeit we speak wisdom among them that are perfect( full grown ) : yet not the wisdom of this world, nor of the princes of this world, that come to nought:

13¶Which things also we speak, not in the words which man's wisdom teacheth, but which the Holy Ghost teacheth; comparing spiritual things with spiritual.
14But the natural man receiveth not the things of the Spirit of God: for they are foolishness unto him: neither can he know them, because they are spiritually discerned.
15But he that is spiritual judgeth all things, yet he himself is judged of no man.

1¶And I, brethren, could not speak unto you as unto spiritual, but as unto carnal, even as unto babes in Christ.
2I have fed you with milk, and not with meat: for hitherto ye were not able to bear it, neither yet now are ye able.

* was Peter born again here .

Jesus cleared up this issue entirely in the book of revelation.
A lukewarm christian can and will lose there inheritance possibly there salvation.
We need to be doers of the word and not hearers only. How many can really say they have been persecuted for his name same?
Contending for the faith is a action not a thought. Perseverance is a struggle of will when subjected through numerous trails.

They replied, “We want to perform God’s works, too. What should we do?” Jesus told them, “This is the only work God wants from you: Believe in the one he has sent.”
John 6:28‭-‬29

You are either misquoting the scripture, or you are inserting your own false interpretation of the verse. The correct interpretation of the scripture is; the fact that you believe at all is the work of God. Not that God wants you to believe.

All men have been given the choice to come to their Maker. God has a wonderful plan for every little baby ever born. No baby was born to burn. Whosoever will may come. God is not willing that any should perish. The call is to all.

Revelation 3:20 Behold, I stand at the door, and knock: if any man hear my voice, and open the door, I will come in to him, and will sup with him, and he with me.

Romans
1:19 Because that which may be known of God is manifest in them; for God hath shewed [it] unto them.
1:20 For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, [even] his eternal power and Godhead; so that they are without excuse:
1:21 Because that, when they knew God, they glorified [him] not as God, neither were thankful; but became vain in their imaginations, and their foolish heart was darkened.
1:22 Professing themselves to be wise, they became fools,

All I did was quote a verse

Then you are studying from a faulty version of the bible. "This is the work God wants from you is to believe" this would make your belief originate in your mind, and be your work, and not God's work. This verse indicates that God's work in you is what makes you believe. I would suggest that you study from a reliable version of the bible.

I'm rubber, you are glue,.......everything you say bounces off of me and sticks to you.