What about John 3:5?
Your thoughts on the meaning of baptism are close to the Orthodox belief. Baptism is indeed a Mystery of initiation into The Church, without which there is no assurance of theosis. The Church however believes that whatever sins the catechumen has are forgiven as a result of the grace of the sacrament. Now obviously with infants this isn’t an issue, but their initiation is.
As to adults, the Fathers taught:
“Faith and baptism are two kindred and inseparable ways of salvation: faith is perfected through baptism, baptism is established through faith, and both are completed by the same names. For as we believe in the Father and the Son and the Holy Ghost, so are we also baptized in the name of the Father and of the Son and of the Holy Ghost; first comes the confession, introducing us to salvation, and baptism follows, setting the seal upon our assent” +Basil the Great
but as to infant baptism:
“If the only meaning of baptism were remission of sins, why would we baptize newborn children who have yet tasted of sins? But the mystery of baptism is not limited to this, it is a promise of future delights; it is the type of future resurrection, a communion with the Master’s passion, a participation in His resurrection, mantle of salvation, a tunic of gladness, a garment of light, or rather it is light itself.” Theodoret of Cyrus
In the later sense, Orthodoxy views baptism of infants in a profoundly different way from the Latin view, which teaches that baptism of infants cleanses them from Original Sin. I am curious. Among Western-non-Latin Christians, is there a belief that Original Sin is cleansed by baptism?
John 3:5 Jesus answered, "Most assuredly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God."
Prior to birth we are surrounded by water. During birth the water breaks and we are physically born. However, we are not spiritually born "born again" until we have complete faith in Jesus.
Among Western-non-Latin Christians, is there a belief that Original Sin is cleansed by baptism?
Not in my Baptist background. We believe Baptism is a public manifestation of a completed act, done to proclaim the new man in Christ. We do not believe it imparts Grace. We believe in the two ordinances (not sacraments because neither imparts grace) communion and baptism.
It's nice to think we might have some things in common.