"At least some of these accounts of the supernatural must be unreliable."
Sure, as with all knowledge, it's up to you to use your discernment, objectively.
"It is purely an act of faith to decide to believe some and not others, since there is no scientific way to validate the claims."
The New Testament documents, at least, contain the plain and often awkward testimony of people who walked with Jesus. The validity of their claims can be investigated according to the historical method, and the textual reliability of the documents themselves can be investigated according to textual criticism, as you know. Above all, this testimony centers chiefly on public, verifiable events (the intersection of Jesus' life with public figures such as John the Baptist and Herod, the trial of Jesus by Pilate, the death of Jesus, the burial of Jesus in Joseph of Arimathea's tomb, the resurrection of Jesus according to eye witnesses, the immediate explosion of the persecuted 1st century church from this point onwards). That is different from "he said/she said".
Further, the faith referred to in these documents is never a blind faith, as people often impute. Rather, it is a faith in a God who is unseen (obviously), founded on a bedrock surety of things heard and seen (eye-witness testimony). The word faith simply means "trust". The question is, are the witnesses reliable? Is their testimony "trustworthy"? Do you trust Paul of Tarsus, a student of Gamaliel (https://en.wikipedia.org/wiki/Gamaliel) and later a converted persecutor? Do you trust his farewell to the Ephesians in Acts 20:13-38? Do you trust Peter, a middle-class fisherman with hired hands? Do you trust John, brother of James, son of Zebedee? Do you trust James, Jesus' half-brother, leader of the early 1st century Jerusalem church?
More than this, the striking thing with the person of Jesus is that he has contemporary witnesses pointing back to him, but he also has the whole weight of the Old Testament documents pointing forward to him centuries in advance, the very purpose for which they exist.
And then you have Jesus' own polarizing words, the genius of his parables, his transcendent teaching ("But I tell you, love your enemies and pray for those who persecute you", "So give back to Caesar what is Caesar's, and to God what is God's"), his own testimony to his Father, and his own testimony to his death and resurrection. Do you trust Jesus or was he a fraud? Do you trust Jesus or was he mad? As an honest observer, his life and his own words allow for not much more choice.
We exercise faith/trust in the laws of physics on a day to day basis, and faith in the knowledge of the past or present, in terms of people we know existed or exist. We never meet them but we can know them through people who did. In the New Testament documents, it's the same principle as you come face to face with Jesus "the Christ".