Philippians 3:15 "Always be prepared to give an answer to everyone who asks you to give the reason for the hope you have"
Luke was a doctor, and a historian, and one of the greatest writters of the Bible in my opinion.
Luke didnt just want us to take his word of it, he starts his Gosple by telling us he "carefully investaged everything from the beginning" so that we would " know certainty of things" we have been taught. Luke 1:3-4
He goes on to tell us that after JEsus suffered, he showed himself to these men and gave many CONVINCING proofs.
ALl of Christianity hings on the ressurection, and Paul said that " without the resurrection of Christ, our preaching is useless, and so is your faith.
The resurrection of Christ is the proof of Christainity.
Now that being said, I will move on here in answer to your questions, to sum it all up in your own words, "why are the "inerrant" testimonies so inconsistent?"
Good question.
Luke, Matthew, Mark, and John all gave differant detales about the resurrection. When you compare the stories of these 4 men, you immediately find differances in the details.ALot of people like you dismiss the accounts of the resurrection because all 4 mens accounts differ from one another.
I say that the differances amongue the 4 accounts are, in fact, a powerful evidence FOR, rather than against the truthfulness of the recorded accounts.
Why?? Simple.
Even though the four accounts differ from one another, they dont contradict each other. Take Matthew. He begins his account of Easter Sunday by saying," After the Sabbeth, at dawn on the first day of the week, Mary Magadlene and the other Mary went to look at the tomb. Matt. 28:1. Mark begins his account by saying, " When the sabbeth was over, Mary magdalene, Mary the mother of James, and Salome brought spices so that they might anoint Jesus' body." Mark 16:1
Matthew has two women visiting the tomb at daybreak. Mark has three. Is that a contradiction>>
No, its just a differance, and differances are not necessarily contridictions.Take this example ok?
Suppose you arrived at church one Sunday to find a visiting minister. You ask the person on your left," Wheres Pastor Smith? She replies," He went on vacation." Then you ask the person on your right,"Wheres Pastor Smith?" He says to you, " He and his wife are on vacation".Would you then exclaim,"THERES A CONTRADICTION HERS< SOMEONES TELLING A LIE!! OF course you wouldnt.
You would easily realize that the ones on your left and right were not making up false and independant stories of one another.Neither, obviously, were they in collusion. They were just relating the SAME FACT from two differant, but noncontradictory views.
DIfferances in the stories are not necessarily contradictions in history. On the contrary, these MINOR differances provide powerful evidence that the accounts are TRUE.
You know, in a live court of law, ( you people are always putting Christianity on trail, hence the phase)

,when you have two or three witnesses whose stories are all presented exactally alike, you begin to suspect that they have gotton together ahead of time to rehearse their accounts. You then begain to stronglt suspect collusion. But, if each person tells the story from their own perspective, each adding differant details and yet not contradicting the testimony of the others, you can more easily assume you are getting a genuine story.