Your distinction between “Adamic” men and “non-Adamic” men is unorthodox and extrabiblical. It is a distinction that the Bible does not make. The word neshamah is used in the Old Testament to refer to any member of the human species (including pagan civilizations such as the Hittites and Canaanites, Deut. 20:16-17) and expanded upon in the Flood account to include any other air-breathing creature. Any other interpretation is simply not in the text. The biblical account does not give any room for such flights of fancy.
I personally eschew all of the doctrines and traditions of men across the board, so calling my beliefs “unorthodox” is of no consequence. They are however, altogether Scriptural and are the leanings I have in the Spirit. As I have testified before, Scriptures are Spiritual per se - they contain the words of God - and therefore, they cannot be discerned like ordinary words. The people Christ is addressing below were physically hearing Him but they could not spiritually hear Him:
Why do ye not understand my speech? [even] because ye cannot hear my word. – John 8:43
And again,
But 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. - I Corinthians 2:14
The significance of earthy genealogies in Scripture begins with Adam and ends with Jesus Christ.
And Jesus himself began to be about thirty years of age, being (as was supposed) the son of Joseph, which was [the son] of Heli, .... [snip] .... Which was [the son] of Enos, which was [the son] of Seth, which was [the son] of Adam, which was [the son] of God. – Luke 3:23-38
And again,
Ye worship ye know not what: we know what we worship: for salvation is of the Jews. – John 4:22
From Genesis to Revelation, the Scriptures are "about" family - God's family. God the Father, God the Son, God the Holy Spirit who makes each of us Christians alive in Him. The meaning of life, the purpose of our existence, is not this heaven and earth but the next heaven and earth when we will be gathered as His family to live with Him forevermore.
From Genesis 2 to Christ, the family story centers on Adam and his descendants. The first narrowing of the family was in the Noah Flood where only 8 of the descendants of Adam survived. The next narrowing was in Abraham’s being called. Then Israel.
And to Israel, God promises because they made Him jealous, He would extend His promise to those who were not a people – which is us. That is the prophesy of Christ bringing in the Gentiles as written in the Song of Moses (Deut 32).
They have moved me to jealousy with [that which is] not God; they have provoked me to anger with their vanities: and I will move them to jealousy with [those which are] not a people; I will provoke them to anger with a foolish nation. – Deuteronomy 32:21 I say then, Have they stumbled that they should fall? God forbid: but [rather] through their fall salvation [is come] unto the Gentiles, for to provoke them to jealousy. – Romans 11:11
And other sheep I have, which are not of this fold: them also I must bring, and they shall hear my voice; and there shall be one fold, [and] one shepherd. – John 10:16
For I would not, brethren, that ye should be ignorant of this mystery, lest ye should be wise in your own conceits; that blindness in part is happened to Israel, until the fulness of the Gentiles be come in. And so all Israel shall be saved: as it is written, There shall come out of Sion the Deliverer, and shall turn away ungodliness from Jacob: For this [is] my covenant unto them, when I shall take away their sins. As concerning the gospel, [they are] enemies for your sakes: but as touching the election, [they are] beloved for the fathers' sakes. – Romans 11:18-28
Thus the Song of Moses is sung in heaven along with the Song of the Lamb:
And they sing the song of Moses the servant of God, and the song of the Lamb, saying, Great and marvellous [are] thy works, Lord God Almighty; just and true [are] thy ways, thou King of saints. – Revelation 15:3
Effective with Jesus, God being enfleshed to atone for our sins, the nature of the “family” is no longer narrowed to those who were descendants of Adam, who was a "living soul" because of the breath of God (neshama). Earthy genealogies no longer matter because God's family now consists of those who were born anew by the Spirit as an adopted child of God.
So also [is] the resurrection of the dead. It is sown in corruption; it is raised in incorruption: It is sown in dishonour; it is raised in glory: it is sown in weakness; it is raised in power: It is sown a natural body; it is raised a spiritual body. There is a natural body, and there is a spiritual body. And so it is written, The first man Adam was made a living soul; the last Adam [was made] a quickening spirit. – I Corinthians 15:42-45 But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his. - Romans 8:9
That which is born of the flesh is flesh; and that which is born of the Spirit is spirit. Marvel not that I said unto thee, Ye must be born again. – John 3:6-7
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: Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God. - John 1:12-13
For ye have not received the spirit of bondage again to fear; but ye have received the Spirit of adoption, whereby we cry, Abba, Father. The Spirit itself beareth witness with our spirit, that we are the children of God: - Romans 8:15-16
And thus the old genealogies which were vital to Adamic men do not apply to us Christians because Our Father art in Heaven:
But avoid foolish questions, and genealogies, and contentions, and strivings about the law; for they are unprofitable and vain. - Titus 3:9
Returning now to the term neshama and what it means vis-a-vis the ancient Jewish understanding of soul and spirit and life:
1. nephesh – the will to live, the animal soul, or the soul of all living things which by Jewish tradition returns to the “earth” after death. In Romans 8, this is seen as a whole, the creation longing for the children of God to be revealed.
And God said, Let the waters bring forth abundantly the moving creature that hath life, and fowl [that] may fly above the earth in the open firmament of heaven. - Genesis 1:20 For the earnest expectation of the creature waiteth for the manifestation of the sons of God. For the creature was made subject to vanity, not willingly, but by reason of him who hath subjected [the same] in hope, Because the creature itself also shall be delivered from the bondage of corruption into the glorious liberty of the children of God. For we know that the whole creation groaneth and travaileth in pain together until now. - Romans 8:19-22
My musing is that the life which is in an amoeba, anthrax spore, daffodil, fish, etc. is in the physical Creation and not the spiritual Creation. There is not an afterlife for each of these autonomous living biological entities but rather as a whole, there will be a new heaven and new earth. 2. ruach - the self-will or free will peculiar to man (abstraction, anticipation, intention, etc.) – by Jewish tradition, the pivot wherein a man decides to be Godly minded or earthy minded.
For God doth know that in the day ye eat thereof, then your eyes shall be opened, and ye shall be as gods, knowing good and evil. - Genesis 2:3 For they that are after the flesh do mind the things of the flesh; but they that are after the Spirit the things of the Spirit. For to be carnally minded [is] death; but to be spiritually minded [is] life and peace. - Romans 8:5-6
My musing is that this is man's conscience, will and mind which sets him apart from other forms of life. He has a sense of right and wrong and he chooses. Among all of life forms, man chooses to honor or dishonor the dead. And he is especially willful and self-serving. 3. neshama - the breath of God given to Adam (Genesis 2:7) which may also be seen as the “ears to hear” (John 10) - a sense of belonging beyond space/time, a predisposition to seek God and seek answers to the deep questions such as “what is the meaning of life?"
And the LORD God formed man [of] the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul. - Genesis 2:7 And when he putteth forth his own sheep, he goeth before them, and the sheep follow him: for they know his voice. And a stranger will they not follow, but will flee from him: for they know not the voice of strangers. – John 10:4-5
My musing is that these are the elect chosen from the foundation of the world. The ones Christ is bringing "home" to be members of His family forevermore. Every man has ruach but not every man has neshama.
And he said, Therefore said I unto you, that no man can come unto me, except it were given unto him of my Father. – John 6:65
4. ruach Elohim - the Holy Spirit which indwells Christians – the presently existing in the “beyond” while still in the flesh. This is the life in passage : "In him was life, and the life was the light of men..." (John 1)
And the earth was without form, and void; and darkness [was] upon the face of the deep. And the Spirit of God moved upon the face of the waters. - Genesis 1:2 But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his. - Romans 8:9
For ye are dead, and your life is hid with Christ in God. - Colossians 3:3
To God be the glory, not man, never man.