If the idea of pseudepigraphy in the Bible is distressing to you, ypu should be warned that almost half the books in the New Testament (13 out of 27) are regarded as forgeries. Only seven of Paul's letters are undisputed as authentic by mainstream critical scholars. Those seven are Romans, Galatians, 1 and 2 Corinthians, Philippians, Philemon and 1 Thessalonians (but not 2 Thessalonians). The Episitles of Peter, John, James and Jude are likewise viewed as 2nd Century epigrapha.
How to reconcile this with inerrancy has no academic answer. The scholars who have concluded the above have almost all been believing Christians and they find personal ways of doing it. usually, they drop the idea of literalism. Many will say that inerrant truth does not have to mean literal truth.
John Dominic Crossan, a New Testament scholar, one of the founders of the Jesus Seminar and still a practicing Catholic (though no longer a Priest) wrote a book called <em>The Power of Parable</em> that you might find helpful in explaining how at least some critical scholars reconcile their commitment to their faith with what they feel is a commitment to the integrity and honesty of their research.
Can you believe the Parable of the Good Samaritan is fiction and still think it has value?
I'd suggest a book called <em>The Power of Parable: How Fiction by Jesus Became Fiction about Jesus</em> by John D Crossan (a famous New Testament scholar, former Catholic priest and still practicing Catholic).
Crossan argues that many of the stories about Jesus should be understood as parables teaching moral lessons. As with the Good Samaritan story, the literal truth of the story is irrelevant.
I say that insisting on a literal interpretation of the Bible is like climbing up a sign post instead of following the sign, or to steal from Bruce Lee, like staring at the finger pointing at the moon instead of looking at the moon.