What exactly are your credentials in Koine Greek of the period to dismiss the most authoritative lexicon for study of the New Testament texts on this matter? In answer to your question, κρατιστος is used within the New Testament only by Luke, occurring here in the preface to the gospel and three times in Acts: (1) in a letter addressing Felix, the Roman procurator of Judea [23:26], (2) in a speech by the lawyer Tertullus to this same individual [24:3], (3) in Paul's address to Felix's successor Festus [26:25]. How you make the argumentative leap from these three uses to the fourth found in Luke as necessarily being a high priest is anybody's guess. You further seem to presume that Luke wrote in a vacuum and that his usage is idiosyncratic when compared to other Greek literature of the period... if this is the assumption, it would be far more reasonable to conclude that the individual addressed in the preface is a Roman official of some sort as Felix and Festus were (a theory that has entertained wider support than yours; see below). As I've already pointed out from BDAG, however, the address was used of individuals of "varied social status" (a point also made by Alexander ) and it was by no means reserved for kings and high priests (Felix and Festus were neither of these, incidentally) as you erroneously suggested.
I have studied Biblical Greek
What words did the Biblical scholars use in translating the four uses in the Greek text in Luke and Acts? 'Most Excellent'
This word was only used by one Biblical author, Luke, so why do I need to go check BDAG for variants in secular Greek literature?
The manner in which Luke uses the Greek, κρατιστος, is clearly established
It is clear that Luke was addressing a dignitary (My reference that it was only for kings and high priests was an incorrect statement)
However, the point is that Theophilus was a person of great importance, which is also critical in dating the Gospel of Luke