Actually I guess I should copy notes here so I have them bookmarked.

1. Passover rebellion: The author, Charles D. Davis, has done lots of work, but fixates on a couple points that he thinks are telling. First, he follows Schurer on putting the Passover rebellion against Archelaus in 4 BC instead of 3 BC, even though he rejects Schurer's compression of events into one month; he expands that passage backwards instead of forwards as if a 3 BC rebellion isn't even being considered. So his reason for holding to a 4 BC rebellion is from a source that he and I both discount; he recognizes the exchange of letters to Rome totally excludes Schurer on this point (though Schurer got other points right).

2. Eclipse: He uses this to follow what he acknowledges to be a minority (against Steinmann) in interpreting the eclipse passage in Josephus. Now for me it's always been obvious that Josephus is describing the end of the priesthood of Matthias and the beginning of Joazar; that this compels him to backtrack "during" that priesthood to mention another priest for a day, Joseph, during "the fast" that obviously means Atonement; and that he then returns to the removal of Matthias, at which time the eclipse happened. But this minority apparently interpreted "But Herod deprived" as "Herod then deprived" as if it isn't a return to the main narrative, and "that very night" (after the removal) as "that same night" (as if referring to the other night mentioned offhand), and created a narrative in which the fast is tied to the eclipse. This allows him to move the removal somewhat earlier than the eclipse of 13 Mar 4 BC, which allows him to pad the months needed to match Josephus's narrative rather than Schurer's construction. The statement "during the winter months of 5/4 B.C. there were no lunar eclipses" seems incorrect since he counted Adar as winter during which the 13 Mar eclipse occurred.

3. Joseph's priesthood: Happened "that very day which the Jews observed as a fast", which obviously refers to The Fast, Atonement, because it's the annual fast that everyone observes (cf. Acts 27:9 putting The Fast in fall). But by tying this fast to the day before or after the eclipse, he thinks he can force the eclipse to be Nisan 14 (thus 23 Mar 5 BC), which is a minor fast. Whiston reports that this event also appears in Mishna and Talmud, and is tied to the stricture of preventing the high priest from sleep for Day of Atonement only. The idea that Matthias had some high officiation to do as to a fast doesn't apply to Nisan 14, when the temple would be filled with Passover lambs (some eating during the day, and those who fasted on that day breaking the fast that evening); it applies to Atonement, when he has very specific complex duties that only the high priest can perform. So the whole idea that we must use the fast as tying it to the eclipse, which then wrests the eclipse away from the flow of the narrative about Matthias's priesthood ending, fails to match the evidence (which is why Steinmann and the majority reject it).

4. Herod at Jericho: He also assumes that the site of this removal, Jericho, must be Herod's winter palace, namely that he is only there in winter. Interestingly, he believes that Herod's later return to Jericho from Callirrhoe happened in Adar II, but the 13 Mar eclipse was in Adar also, so nothing prevents it from being the one that occurred the very night Herod deposed Matthias. (Perhaps he might object that Herod would not have returned to Jericho later in the year, but that is an unstated proposition and it's unclear to me why this hypothetical would be impossible.)

5. Varus succeeding Saturninus: He emphasizes that this happened in the year 7-6 BC based on coin evidence, and Josephus's first mention of Varus is with Antipater's presumptive appearance before Herod, which he puts in late 5 BC. He regards this as a discrepancy, but it would be simple to hold that Varus had previously succeeded Saturninus but his appearance before Herod is the first time he is mentioned. It seems this is answered by his possible reading "Varus (who was Saturninus' successor) was in Jerusalem".

Sounds like by ignoring Whiston's chronology with the eclipse in 4 BC and the Passover rebellion in 3 BC (though interest in it has been revived by Hoehner, Lanser, etc.), he's making additional special pleadings by reference to Jericho being a "winter" residence and the "fast" of Joseph being useful for dating the eclipse rather than a reference to Atonement as it is in the Mishna.