First up, I believe that the two Crucifixion pieces - one in the Gospels and the other in Josephus - are different in kind. The Gospels Crucifixion originates in GJohn. It contains material from Suetonius and, perhaps more importantly, material from Tacitus.
The Roman soldiers look up to the three on the crosses and they are indeed Galba, Otho and Vitellius and all three end up dead, dead and, as a change of pace, dead. The Tacitus material (_Histories..._, Book 4), records the key material of the reunification of the Legions with Mucianus calling the loyalty of "...the same oath to the same Caesar...". Tacitus even gives a brief reason for "Jesus" being 3 days and 3 nights in the earth. The Legions are offered a retirement package that includes land for those who accept and this is completely rejected. "It is finished!" That is, the Roman Civil War and this is Tacitus' contribution to the Gospels.
Meanwhile, Titus/Caesar is at the razed Temple area and the language is most interesting:
"So when they had all these honors bestowed on them, according to his own appointment made to every one, and he had wished all sorts of happiness to the whole army, he came down, among the great acclamations which were made to him, and then betook himself to offer thank-offerings [to the gods], and at once sacrificed a vast number of oxen, that stood ready at the altars, and distributed them among the army to feast on. And when he had staid three days among the principal commanders, and so long feasted with them, he sent away the rest of his army to the several places where they would be every one best situated."
The Noir History of Jesus-Archelaus, which provides a wrapper for most of the other Gospel Stories, finds the Temple Priests mere moments away from seeing the "Splendor of God" as the Temple is expected to be cleansed and rededicated by God as promised in,for example, Leviticus 28. They met death instead.
Here, Titus "comes down" as acts as the High Priest of the New Church, offering sacrifices at the altars and gives the meat to the New Servants who will live eternally as promised by Titus in one of the many speeches recorded by Josephus. Here is the Roman view of the "Splendor of God".
In discussions with Joe Atwill, the OTHER Crucifixion, found in Josephus, is about a very tightly worded parallel between the Crucifixion where two die and one survives, and the Physician Pedanius, who is able to handle the very powerful root found in Jerusalem. Here is the "Pruning" work that is done.
In a few years, when more of the material has been cross referenced and mapped - no pun intended - I believe we shall have an understanding of just how far this joke went:
© Charles N. Pope, US Library of Congress. All rights reserved.