What Dave argues is a quite venerable position; Harnack held it at one point, and when it was first presented to me as an undergraduate I was content to do so as well. Within a Lonerganian framework it falls properly within the functional specialty of interpretation: making intelligible to oneself the meaning of the text, which is to say to construe what the writer(s) intended to communicate. Of course it goes without saying that some texts are ultimately unintelligible, but all things being equal an interpretation that can, without doing severe injustice to the data, offer an intelligible reading of the material is to be preferred to one that cannot. And that's where I'm afraid that the "Luke didn't want to mention Paul's execution because it was counter to his efforts to present him as innocent" begins, for me, to break down.
It strikes me as a bit odd that Luke would be at such pains to show that Paul was innocent in the proceedings that took place in Jerusalem and Caesarea but make no effort to argue the same with regard to the proceedings in Rome. If Luke is so keen to highlight Paul's innocence and if he is writing after Paul's execution, then it seems a major lacuna not to offer an explanation of how it is that Paul, an innocent man, could be put to death by the empire. If it is the case that he could expect that his audience doesn't know that this was Paul's fate then could he reasonably expect that they knew of his earlier legal strugges? And if on the contrary he could reasonably expect that they did not, and if he wants to highlight Paul's innocence, and if he does so by excising events--such as the execution--that present him as in trouble with the authorities, then why does he raise the matter of these legal struggles at all? It's sort of like arguing at great length that a man is innocent of those speeding tickets yet altogether ignoring the fact that he is languishing in prison for murder. In such a reading then, at the very least Luke, would seem to be majoring in the minors. For the reader of, say, 85, the ending is going to raise more questions than it provides answers, with specific regards to Paul's legal innocence.
This problem disappears entirely if Luke finishes Acts towards the end of or not long after Paul's two years under house arrest in Rome. In that case one could affirm with Dave that Luke aims to highlight Paul's innocence, and in the process not generate such a lacuna. Luke's aims, as identified by Dave, become infinitely more intelligible. And remember that Luke does not shy away from depicting great figures of the faith put to death, such as Stephen and James son of Zebedee; he simply frames their deaths as the result of human malice. Given that Paul is executed under Nero, and given that c. 70 and later the Flavian dynasty is at pains to represent Nero (rightly or wrongly) as a tyrant, and given that in fact he is remembered as having unfairly persecuted Christians at Rome, it would not have been too difficult for Acts to frame Paul's death in a manner comparable to how he frames that of other martyrs. And in any case, if he can present Jesus the crucified as an innocent man then it seems that he could do much the same for Paul the beheaded.
In the final analysis of course the above is not a definitive argument. Dave's position is not impossible. I just think that on the balance of the data a Luke who wrote Acts c. 63 operates more intelligibly than one who wrote Acts c. 85. And ultimately that is my only concern here: rendering intelligible these ancient writings, and having thus done so rendering intelligible the world in which they were written. I am aware of course that there are always those who will co-opt such arguments to support various conservative theological and indirectly (given the confluence of theology and politics in certain places in this world) political ends; I cannot help that. All I can say is that they are mistaken to think that an Acts written c. 63 C.E. is somehow more conducive to such ends. Indeed, an Acts written in 62 is no more intrinsically likely to be more historically "reliable" (a somewhat problematic historiographical category anyways, although one that I am guilty of employing in my own work) than one written c. 85, and conceivably quite the opposite: time and distance from events have a way of calming passions that might otherwise interfere with reasoned reflection upon and construal of experiences, either one's own or that which one has learned about others. And moreover, few Christian doctrines turn upon the historical reliability of the Acts; the edifice of Christian theology does not topple if Paul never visited Athens or Peter never baptized Cornelius. My argument is no more calculated towards theologically conservative ends than is James Crossley's argument that Mark wrote his gospel c. 42 (and if you want to call James Crossley a theological conservative, please, be my guest); and to let fear of conservative co-optation drive my exegesis and historiography is to let such conservatives control the discourse, and I'm not quite prepared to do that.