Respectfully, you are avoiding the issue altogether by seeking to change the subject. At the moment, I'm dealing only with the supposed "Gospel of Luke" and other gospels, not with Acts (I will deal with Acts later). And, regarding the former, you've not addressed any of my contentions and instead argue from presupposition.
For instance, you presuppose that your "Dr. Luke" actually wrote the Gospel of Luke. But, what evidence do you have for that? The Gospel of Luke, like all other gospels, was written anonymously. It contains no claim of authorship. Zero. None. Nada.
Furthermore, if your claims that (1) the Gospel of Luke was written by the same author as Acts, and (2) that the author of Acts accompanied Paul on his journeys (or at least starting where the "We Document" begins), then why in the world would that author not have mentioned that fact at the beginning of his gospel!. If the author of Luke was indeed an eyewitness to Paul's missionary journey, why does he not simply say that?! It's inconceiveable that someone whose stated purpose in writing the gospel is so that others like Theophilus "may believe with certainty" fails to cite even a single one of his sources, especially when one of those sources is, by your theory, Paul himself, the greatest of the Apostles!
Additionally, as I will explain when I get to the chapters on Paul, Paul almost certainly was not the source for any of the biographical details regarding Jesus's life contained in Luke and the other gospels. In his authentic writings, Paul seems to know virtually nothing about Jesus time on earth--he never mentions the Virgin Birth, never mentions his miracles (other than the resurrection which, as I will show, Paul understood differently), and he never quotes Jesus's sayings and teachings (other than at the Last Supper) even when doing so would cinch his various argument with "those from James". Much more on this later. Suffice to say for now that Paul was not the source of the biographical details of Jesus's life.
So...who was? We simply don't know. Why? Because Luke refuses to tell us. Were a Mormon or a Muslim to offer up such flimsy "evidence" for his or her beliefs, or for the authorship of the Book of Mormon, you'd make a laughing stock of him/her, and rightly so.
And, here's the bigger question: As regards "proof" and "evidence", why are we simply left to "settle" for "what history will give us", as you suggest? After all, God can, and has, intervened in history, right? If he really intended to make the salvation of future generations of Christians contingent upon believing and accepting some official written biography of Jesus's life, he certainly could have made that biography much more compelling, right? That he didn't suggests either that God is a jerk, that he "works in mysterious ways" (which tells us absolutely nothing), or that this was never God's intention.
So, I'm not "rejecting" the supposed Dr. Luke's "first rate testimony". I don't even know that it was Dr. Luke's testimony at all, and you don't either. I have no doubt that whoever wrote it preserved some actual history. However, unlike you, I treat "Luke's" historical account just as I would any other account of "history". In deciding what to believe and what not to believe, I look to who wrote it (which we don't know) to determine viewpoint and bias, I look to the author's sources (which we likewise do not know) to determine the same, I look to my own common sense and recognize obvious myth-making (just as you do when you read about the gods of other religions), and I employ all the aids of textual criticism. And I do much more to tease out the truth.
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.
You wouldn't accept similar "logic" from the proponents of any other religion, and so you shouldn't use it to defend your own.
Again, please be patient. I can't dismantle your entire world view with a single post. Rather, I have to set the stage and take it one step at a time. In that regard, it would be most helpful if you would resist "leaping ahead" for the moment. By that I mean this: If you wish to continue this side bar dialogue, it would look be most helpful if you would take my contentions in my chapters and actualy deal with them, as best you can, from my frame of reference. If you can turn my own logic against me (as I regularly do your's), then you win. For instance, I contend that none of the gospels can be shown by anything other than "church tradition" to represent "eyewitness accounts", that all of them were written anonymously and that the only sources that we have for attributing them to Matthew, Mark, Luke and John are either completely unknown or highly dubious. Do you disagree with any of that? Do any of them actually claim authorship and I simply overlooked it? Do any of then cite their sources? Do we have a reliable basis for attributing authorship that I have missed? If so, please do explain. That would be most helpful. These are the types of discussions that it would benefit us as we move forward.
But, if I'm right that they were written anonymously, that they don't cite sources, and that we only attribute them to certain authors as a result of "church tradition", then admit that too. That's fair. Once the truth is on the table, we can deal with it. You can then decide whether or not you'd accept the "church tradition" explanation from a Mormon or a Muslim who sought to use it in defense of their holy texts. If you wouldn't, then you can just concede that your faith is "blind" and we can move on. And if you would, then you can just concede that you have no rational basis for favoring your religion over their's--it's just a matter of whether or not "the spirit moves you".
And...that's okay. It's okay to have blind faith. It's okay to be a "spirt moved me" kind of guy. You'd be in great company with the greatest of Christian apologists over the ages.
You do know that Paul mentions these gospel. and what you do not realise is that paul knew jesus brother james.