The first paragraph from Luke
Many have undertaken to draw up an account of the things that have been fulfilled among us, just as they were handed down to us by those who from the first were eyewitnesses and servants of the word. With this in mind, since I myself have carefully investigated everything from the beginning, I too decided to write an orderly account for you, most excellent Theophilus, so that you may know the certainty of the things you have been taught.
The first paragraph from Acts:
In my former book, Theophilus, I wrote about all that Jesus began to do and to teach until the day he was taken up to heaven, after giving instructions through the Holy Spirit to the apostles he had chosen. After his suffering, he presented himself to them and gave many convincing proofs that he was alive. He appeared to them over a period of forty days and spoke about the kingdom of God.
Taken together these leave no doubt that the author intended Luke and Acts to be two halves of the same contiguous historical account. That coupled with his first hand accounts in the parts where he was involved directly constitutes plenty of evidence that these books were authored by the very companion of Paul that Paul references in many of his letters.
Asking questions like "why in the world would Luke not have mentioned that fact at the beginning of his gospel!" is pointless. The answer is simply, "Because he didn't". There are thousands of ways to write an account and they don't become invalid because an author chooses to do it differently than how you would have done it. A simple explanation is that everyone in the Christian communities all around the Mediterranean knew Dr. Luke, including Theophilus to whom these letters were written. (Whether Theophilus was a single person or a category of "God loving" people, it's not hard to imagine that Dr. Luke would not consider it necessary to introduce himself to any of his target audience.)
Most of the New Testament books have a similar back story - they were delivered into the care of existing Christian communities who recognized their authenticity and preserved/distributed them. Later, when the final canon was formally recognized, books that did not have this pedigree were omitted.
For example, in Paul's letter to the Colossians, he ties a lot of connections together giving us a virtual who's who of the early churches (including more info about Mark who figures prominently in the early Chapters of Acts):
Colossians 4:10-14
My fellow prisoner Aristarchus sends you his greetings, as does Mark, the cousin of Barnabas. (You have received instructions about him; if he comes to you, welcome him.) Jesus, who is called Justus, also sends greetings. These are the only Jews among my co-workers for the kingdom of God, and they have proved a comfort to me. Epaphras, who is one of you and a servant of Christ Jesus, sends greetings. He is always wrestling in prayer for you, that you may stand firm in all the will of God, mature and fully assured. I vouch for him that he is working hard for you and for those at Laodicea and Hierapolis. Our dear friend Luke, the doctor, and Demas send greetings. Give my greetings to the brothers and sisters at Laodicea, and to Nympha and the church in her house. After this letter has been read to you, see that it is also read in the church of the Laodiceans and that you in turn read the letter from Laodicea. Tell Archippus: "See to it that you complete the ministry you have received in the Lord." I, Paul, write this greeting in my own hand. Remember my chains. Grace be with you.
Then we have Peter's endorsement of the letters of Paul from 2 Peter 3:15 which even acknowledges them as Scripture:
Bear in mind that our Lord's patience means salvation, just as our dear brother Paul also wrote you with the wisdom that God gave him. He writes the same way in all his letters, speaking in them of these matters. His letters contain some things that are hard to understand, which ignorant and unstable people distort, as they do the other Scriptures, to their own destruction.
Formally citing sources would be nice but it is not expected in informal letters characteristic of the first century and the New Testament is a primarily a compilation of such letters. Nevertheless, there are plenty of cases where specific well-known individuals were mentioned as the primary actors. They were all still around during the days when these letters began circulating and would surely have objected if these accounts were in any way inaccurate.
So it all ties together to form the single most intensely examined mosaic of documents in the history of mankind. If the best you can do is demand ever more and more evidence for the mere reason that something is not there that you think "should" be there to remove the last of your doubts, then I'm afraid you are wasting your time.
Show me concrete evidence that these are one giant set of interconnected fraudulent documents by citing other more authoritative historical documents that plainly contradict them. Pointing out how the documents we have could have been made evidentially stronger is no evidence at all. We are only quibbling about our individual preferred Thresholds of Belief.
I have already stated the obvious principle that God did not intend to provide iron clad proof for you. If He did he could have provided all kinds of ongoing supernatural evidence. Your failure to find enough proof to satisfy you merely places you on the other side of whatever threshold the Lord decided would meet His needs to separate sheep from goats via His definition of believers vs. unbelievers.
As for your statement that
What I don't do is presuppose divine inspiration, presuppose infallibility, and give the author every bit of the theological and historical doubt. I don't contend that a book written by an unknown author citing unknown sources and claiming miraculous things is infallibly true.
I don't do that either. As I have stated elsewhere, I first find the collection of books that make up the Bible to be merely credible. Then I have those credible authors quoting Jesus verifying that "Scriptures cannot be broken" indicating that God has been supernaturally preserving them (as the Dead Sea Scrolls prove pretty convincingly). Then I have the credible authors of the Gospels testifying that the scriptures themselves are inspired (God breathed). That's how I get to infallibility. It is not my initial assumption.
From Paul:
All Scripture is God breathed and useful for teaching, correcting, rebuking, and training in righteousness so that the servant of God may be complete, thoroughly equipped for every good work. - 2 Timothy 3:16-17
From Peter:
For we did not follow cleverly devised stories when we told you about the coming of our Lord Jesus Christ in power, but we were eyewitnesses of his majesty. He received honor and glory from God the Father when the voice came to him from the Majestic Glory, saying, "This is my Son, whom I love; with him I am well pleased." We ourselves heard this voice that came from heaven when we were with him on the sacred mountain.
We also have the prophetic message as something completely reliable, and you will do well to pay attention to it, as to a light shining in a dark place, until the day dawns and the morning star rises in your hearts. Above all, you must understand that no prophecy of Scripture came about by the prophet's own interpretation of things. For prophecy never had its origin in the human will, but prophets, though human, spoke from God as they were carried along by the Holy Spirit. -- 2 Peter 1:19-21
You still avoid my questions. What evidence do you have to attribute the Gospel of Luke to Dr. Luke? None. You simply infer that Luke was written by a companion of Paul. There is no strong basis for that inference. Possible? Yes. But equally possible otherwise.
Regarding the "We Document", there are far more likely explanations than yours. Scholars who read the original Greek recognize instantly that the author of the first part of Acts (that talks about "they") and the second part (the "We Document") were not one and the same. The style and language are completely different. They were later severely edited and combined into one document to serve the purposes of Orthodox editors. Much more on this later.
I just spent hours giving you tons of evidence.
I await this scholarly proof you claim to have.
again you dodged what he represented to you. As I said before they've found the earliest manuscript of corinthians. That dates back to 32 AD. 2 years after christ death. Secondly that manuscript had a qoute from luke. SO paul indeed read the gospels.