Okay, this might be something:
The OAHSPE Bible mentions Crite three times:
"Thoth sent the following message to Looeamong, to wit:...But, behold, I labor against Gods who have the advantage of me. The Chine'ya rebel
Gods and the Vind'yu rebel Gods, that fled from the Triune kingdoms in the east, have
taken upon themselves names popular with mortals. Witness these names:...Pherna, alias
Holasa, alias Iao, alias Crite, alias Thammus..." (pg. 958)
"For one year and five months the balloting lasted, and at that time the ballot rested
nearly equally on five Gods, namely: Jove, Kriste, Mars, Crite and Siva. And here the
ballot changed not for yet seven time more, which was seven weeks." (pg. 963)
The next question was, what mortal representative should be chosen? The first ballot brought out the following men: Zarasthustra, Thothma, Abraham,
Brahma, Atys, Thammus, Joshu, Sakaya, Habron, Bali, Crite, Chrisna, Thulis, Witoba
and Speio. Besides these, there were included in the ballot, forty-six other men, who
received a small number of ballots each. (pg. 963)
As can be seen, several of the other crucified figures mentioned by Higgins and Graves also appear, such as Atys, Chrisna (Krishna), Witoba and Thulis.
If the OAHSPE is reliable in any sort of way, then that means that Crite can be identified with Thammus1, AKA Tammuz, who, according to Higgins, is connected to St. Thomas:
"...Is there not great room for suspicion, that this Thomas was the Tamus for whom the women of Judea
wept, and that his followers were not Christians, but Crhj-tians, followers of him of whom the Erythræan
Sibyl prophesied?...The Portuguese finding these Christians worshiping and bewailing a Thomas or Tamuz—put to death at the
vernal equinox, and after three days rising again to life, as I shall shew in a future book—to whom were
attributed all things which were attributed to Jesus Christ, settled it instantly, that there was a mistake
ignorantly made between St. Thomas (who must have gone to India as they believed) and Jesus Christ—a
mistake made before by Jerom..." (pg. 666)
However, author Acharya S suggests in an essay on Beddru (also on the list) that Beddru is a printing typo and is meant to be Beddou, who she identifies with Buddha, so if Crite isn't an invention of Graves', it's possible that it's also a typo. As was pointed out somewhere on the internet, this would mean that Buddha appears more than once on the list, under different names. If the OAHSPE's interpretation holds any water, then the same can be said of Tammuz.
As it turns out, in the second volume of Anaclypsis, the following is written:
"I now beg my reader to look back to Vol. I. pp. 549-553, and there he will see the account of the prophecy of Apollo of Miletus...In this country there was a place called Thamas...also...and the island of Crete, called Candia and Icriti. I think in Apollo Didymaeus and the oracle of the incarnate person crucified by the Chaldaeans...and Patrick to Ireland, who brought the mythos of the God incarnate crucified by the Chaldaeans - the God Icriti or Critika2, which was both bull and ram3 - the God alluded by Apollo of Miletus." (pg. 117)
This Icriti4, as was written in Volume I, was crucified by Chaldean judges:
Lanctatius makes the Apollo of Miletus say, "He was a mortal according to the flesh; wise in miraculous works; but, being arrested by an armed force by command of the CHALDEAN judges, he suffered a death made bitter with nails and stakes."5 (pg. 543)
"If my reader look back to Book IX. Chap. X., he will find a prophecy by Apollo, of Miletus, of a divine incarnation crucified by Chaldean judges. There were the Chaldaeans of Colida…It was the crucifixion of Crisen and Salivahana and St. Thomas, of the Christians of Crisen." (pg. 810)
"Lactantius makes the Apollo of Miletus say, "He was a mortal according to the flesh; wise in miraculous works; but, being arrested by an armed force by command of the Chaldean judges, he suffered a death made bitter with nails and stakes. In this, of course, devotees will see nothing but a Gentile prophecy of Christ...The reference to the Chaldean judges shews, that this can have no reference to the crucified saviour of our Bible."" (pg. 584)
1 That Thammus and Crite appear as separate entities in the third section appears to be because that section refers to mortals, many of whom are named after gods.
2 On Icriti and Crite: In Hebrew, "Ikriti" means "of Crete" (for example, Rabbi Shmaryah HaIkriti, who, coincidentally enough, was put to death on the assertion that he had claimed he was the Jewish messiah). Crite is of course very similar to Crete, and Higgins was known to have mixed and matched multiple languages and multiple varying spellings of different words, so perhaps the typo came from here.
3 On "the Bull and the Ram" - this appears to be a reference to vol. I, pg. 231:
"But the word Ram, ראם ram in Hebrew [actually pronounced Re'em] means both Bull and Ram. This arose, I suspect, from the Indian incarnation of Rama, who preceeded Cristas. In fact he was the incarnation of the Neros when the Sun left Taurus and entered Aries; thus he was incarnate in the signs of both the Bull and the Ram.
Re'em in Hebrew refers to both the modern animal the Oryx and the mythic Re'em creature, which is widely believed to have been some sort of wild bull.
This, in turn, appears to refer to a running idea in vol. I of the bull and the ram representing God:
"...and this may account for the transfer of the festival of Taurus to that of Aries...It is pretty evident from the Paschal feast, the sacrifice of the Lamb, the change of the beginning of the year to the first of Aries, the anger at Aaron's Bull or Bulls, the going back of the Israelites to the Bulls of Bethavon, בית אן bit an, etc, a great part of Moses's object was the change of the festival of the equinox from Taurus to Aries. I cannot help suspecting that in very anceint times a human being was sacrificed at the Pascal festival by some devotees, and that the story of Abraham's sacrifice of Isaac was the mythologic mode of describing the change, either from this worship, or from the offering of the bull or calf, to that of the Lamb, perhaps of both. The simultaneous existence of the worship of the sun in Taurus with the sun in Aries...Thus we find the festival of Taurus continued along with that of Aries in Britain...In Egypt they appear to have gone on amicably. And we have Osiris, Apis, Serapis, and Jupiter Ammon..." (pg.256)
"To return to the word Baal. The word בעל bol, called by us Baal...בעל bol is also called אלהים aleim [actually pronounced Elohim]...God was originally called בעל Bol, Thou shalt no more call me Baali. He was afterwards called...ie [reference to the tetragrammaton]...and was the root of the word Iaw, or Iao-pater, Jupiter, and in Egypt, with the head of a ram, was called Jupiter Ammon [possibly Amun?]. The followers of Baal were the worshipers of the sun in Taurus: those of Iao of Ammon - of the sun in Aries. From the word בעל Bol probably came our word Bull. Here the struggle betwixt the two sects of Taurus and Aries shews itself."" (pg. 258-259)
4 The description of "Crite" or Icriti in Graves' book appears to have come from the following passage:
"In this ceremony of sacrificing the lamb the devotees of India chant with a loud voice, When will it be that the Saviour will be born! When will it be that the Redeemer will appear!" (pg. 261)
In vol. II, pg. 117, in a footnote on Icriti, Higgins wrote:
"Evidently the Indian Kritika6."
Meaning that Higgins identified the Indian savior with the Cretan/Chaldean Icriti, which explains "Crite"'s description in Graves' book.
5 Lactantius, the Divine Institutes, Book IV. Lactantius makes out this prophecy to be about Jesus, but Higgins refutes that because of the reference to Chaldean judges as the crucifiers (and not Romans). Either way, this means that the Milesian oracle spoke of an event that had happened long before (as opposed to foreseeing the future).
6 On Kritika in India and Crete: Krittika is the Indian name for the Pleione star cluster and is also the name of the female goddess-personification of the cluster. Kritika is the name of a type of traditional Cretan music.
In short, "Crite" appears to have been a Cretan deity or deity-incarnate who was prophesied by Apollo of Miletus to being crucified by Chaldean judges, which supposedly is exactly what happened.
Note: According to Wikipedia, Babylonian history can be calculated through five different chronological calculations (ultra-short chronology leading up to ultra-high chronology), so it's hard to pinpoint what exactly may have happened in 1200 BCE, if that's even the correct date and if anything related to the crucifying of a Cretan happened at all.
A few possibilities: 1. Collapse of Hittite power in Anatolia with the destruction of their capital Hattusa. 2. Massive migrations of people around the Mediterranean and the Middle-East. See Sea People for more information. 3. Aramaic nomads and Chaldeans become a big threat to the former Babylonian and Assyrian Empire. 4. Migration and expansion of Dorian Greeks. Destruction of Mycenaean city Pylos. 5. Final destruction of the major Mycenian city excavated at Iklaina.
As can be seen, circa 1200 BCE there were many great upheavals both in the area of Crete and its people (Mycenaeans, Sea People, etc) and in Babylon. It's possible that in order to reach new land, the displaced Cretans traveled through Babylon and were attacked by the Chaldeans, but this is just a guess.