One can hold that there is indeed Original Sin without assuming the nature of man changed. One might say instead, that the image of God was marred in man, like a coin covered in dross and scored with cuts. But the image remained. The nature - how man was made - did not differ, but his mode - as the Fathers say (I'm leaning heavily on Maximus the Confessor here) changed with the fall. So he operated as a beast though he was a man.
It follows therefore that reproduction - and not only physical reproduction but also parentage through fallen adoptive parents - transmits not merely the effects of previous sins on the bodies and souls of the children and parents, but also re-imprints the patterns and habits which foster the disease.
It then therefore follows, that God had to raise up righteous seed - those who were free from habitual sin and receptive to God's help - and that these, and in particular the Mother of God - could and would be able to accept the Son of God as a child and raise him.
This except gives an idea of the Orthodox position vis a vis 'sinful nature':
...Every created nature is made to live in communion with God. Human
nature itself lives in communion with God. Our fall does not consist
in becoming something other than human – we have yet to become truly
human. Thus St. Paul says: “Man is the glory of God” (1 Cor. 11:7).
And St. Irenaeus says, “The glory of God is man fully alive” (Adv.
Her. 4.34.5-7). Our becoming truly human would mean the restoration of
our true integrity – we would live in accordance with our nature and
praise the Lord without ceasing. The natures of all creation
ceaselessly praise God by their very existence. Our struggle is to
rejoin the song of creation with the whole of our being.
So it is not the nature that changes, but whether those hypostases - concrete individuals - live in accordance to how they were made. Original sin constitutes a departure from this way of being at the very outset of human existence that affects the lives of every descendent of Adam and Eve.