As I read through the work of Douglas Campbell on Pauline chronology, I cannot but think that he has placed himself in a position where his judgments collide as described above. He argues that Paul's flight from Damascus (cf. 2 Cor. 11:32-33) can only have occurred between late-36 and early-37. More precisely, he finds himself compelled to narrow this time frame down to late-36, in order to accommodate the data from Acts. He also argues that Paul must have appeared before Sergius Paulus (cf. Acts 13:7) during or less than a year after the reign of Tiberius (which ended on Mar. 16, 37). This leaves a very small window for Paul to appear before Sergius Paulus. Not an impossible window: there is as much as a year-and-a-half for Paul to travel from Damascus to Cyprus, with a visit to Jerusalem (cf. Gal. 1:17-18, which Campbell supposes refers to the same course of events as 2 Cor. 11:32-33) and then presumably also to Cilicia (cf. Gal. 1:20), then Antioch, and then to Seleucia (presumably Seleucia Pieria, Antioch's port), and then to Salamis in Cyprus (cf. Acts 12:25-13:5, which Campbell treats as an itinerary for Paul's journey to Cyprus, in fact adducing sailing conditions from Seleucia to Salamis as evidence that this journey occurred earlier in the year rather than later).
In order to reckon with the tight fit of his chronology, Campbell argues that Paul probably fled Damascus in late-36, then went to Jerusalem for a fortnight, then went to Tarsus (in Cilicia), then wintered in Antioch after the fortnight that he spent in Jerusalem (as per Gal. 1:18). That can place him in Salamis early in the new year, although one suspects that he wouldn't have arrived much before mid-March, after the sailing season opened on March 10. This puts his likeliest early arrival, on Campbell's own account, probably around the same time that Tiberius dies. Given Campbell's insistence that Sergius Paulus was governor in Cyprus for less than a year after Tiberius's death that leaves a very tight time frame indeed.
Now, again, Campbell's account is not physically impossible. It is quite conceivable that Paul could set out from Damascus by late-36 and carry out the proposed travels in the time span allotted. That is to say, if the data necessitated that Paul did so then we would justified in judging that he did. Campbell's work is marked by a laudatory attention to detail in terms of such realities as travel time, so we shouldn't be surprised that he has done his homework in this regard. The difficulty that I face is that I'm not sure that the data necessitates the chronology that he proposes, and in fact I would suggest that the data militates against it. First, I am not entirely persuaded that the data requires that Paul left Damascus no earlier than late-36, although I will acknowledge that here Campbell is on the strongest ground. Second, Campbell bases his argument that Paul must have appeared before Sergius Paulus during or shortly after the reign of Tiberius on his reading of the Chytri inscription, but he himself admits that it could be referring to Gaius instead of Tiberius, which would allow for Paul before Sergius Paulus as late as 41, and it has often been argued by others that the inscription refers to Claudius, thus allowing for as late as 54 (and in fact, if we allow for the possibility that Sergius Paulus remained governor for up to just less than a year after the death of the respective empire, then we have to reckon with much of 55 with reference to Claudius). Third, he must suppose that Luke dislocates his material temporally without any real notice, but as I argued in my penultimate post prior to this one I think that the evidence militates against this supposition.
I have found it to be a general rule in chronological work that when my judgments on two or more matters require me to posit a very chronologically tight series of moves on Paul's part (or that of any other figure) it is typically a sign that my judgments on one or more of these matters is mistaken. Such chronological fit thus becomes a sort of canary in the coal mine for a problem in my synthesis of various matters. Whilst Campbell's arguments with regard to Paul's movements in late-36 through early-37 are not impossible, I am not at this point optimistic about the canary's health.