The Bible and Josephus agree per Jeremiah 52:28-30 that Nebuchadnezzer only took captives in his 7th,18th and 23 rd year.
Not saying this isn't all quite confusing because of the various versions, but here is the basis for believing there was an 7th and 8th year deportation.
Josephus says that Ezekiel was part of the deportation of 3000.
"...he also took the principal persons in dignity for captives, three thousand in number, and led them away to Babylon; among which was the prophet Ezekiel, who was then but young." Ant. X.6.3.
The Bible at Jeremiah 52:28 says those taken into exile in the 7th year were 3023 Jews. Thus this is the deportation of Ezekiel of these deported with just 3000. Jehoiachin was taken later in the 8th year of Nebuchadnezzar near the very end of the eight year and almost the ninth year. This is when over 10,000 were taken into captivity and thus not part of the 7th year deportation where only 3000 were taken captive. But to support this, if the captivity of Jehoiachin basically paralleled the 9th year of Nebuchadnezzar and as well the rule of Zedekiah, then there would be an 8-year gap. Thus when Jerusalem fell in the 19th year of Nebuchadnezzar, it was already the 11th year of Zedekiah.
But if Ezekiel correspondingly were deported the year before, this would be his 12th year of exile. Thus we note at Ezekiel 33: 21 "At length it occurred in the twelfth year, in the tenth [month], on the fifth day of the month of our exile, that there came to me the escaped one from Jerusalem, saying: “The city has been struck down!”
This indicates that the the word that Jerusalem had fallen reached Ezekiel in the 10th month of his 12th year of exile. The trip from Jerusalem to Babylon is about 5 months, thus the city fell in the 5th month and now it's the 10th month of the year in the 12th year of exile. This is consistent with Ezekiel being deported near the very end of the seventh year as was usual for Babylon to deport near the "turn of the year". That being the case, most of his first year was during the 8th year of Nebuchadnezzar and thus there is 7-year difference. 12 plus 7 is 19.
The other issue is that when Daniel went before Nebuchadnezzar in his second year, Nebuchadnezzar did not know Daniel. Daniel and his companions were to spend three years before being presented to the king of Babylon. After being pesented to Nebuchadnezzar he found Daniel and his three companions wiser than all the men in Babylon and was very pleased with them. When he had the dream, therefore, he would have consulted Daniel right up front if not first. Why would he order killing all the wise men of Babylon without consulting Daniel? The reason why, is because Daniel's three years were not completely up yet and Nebuchadnezzar hadn't seen Daniel yet. Daniel and the other three were going to get killed as part of all the wise men though. So he asked for an audience before the king for the first time.
So if Daniel hadn't quite finished his three years of training by the second year of Nebuchadnezzar it indicates that Daniel must have arrived in Babylon less than three year earlier. If per custom, Daniel were deported "at the turn of the year" of the Accession Year of Nebuchadnezzar, and arrived at Babylon 5 months later, and his three years counted from that point, then Daniel's three years would have begun say about the begining of the 5th month of the 1st year of Nebuchadnezzar. His first year would have been completed by the 5th month of the 2nd year of Nebuchadnezzar, his second year by the 5th month of the 3rd year of Nebuchadnezzar and his 3rd year not until the 5th month of the 4th year of Nebuchadnezzar. But even is Daniel had been deported at the very beginning of the accession Year of Nebuchadnezzar, his 3rd year would not have been completed before the say the 6th month of the 3rd year of Nebuchadnezzar.
So this is consistent with Daniel still being in training in the 2nd year of Nebuchadnezzar who apparently had not seen him as yet.
If as you say, the reference about Daniel being deported in the "third year of the "kingship" of Jehoiakim, really means the third year of his vassalship, which began per you (if I'm reading correctly) not until the 4th year of his kingship which began the vassalship, and thus the 3rd year of his vassalship was actually the 7th year of Nebuchadnezzar, then how is it that Daniel is before the king in the second year of his kingship not having been seen by him yet?
You want to make the 3rd year of the Biblically stated "kingship" of Jehoiakim really be a vassalship, and then claim that somehow, the "second year" of Nebuchadnezzar likewise wasn't really his second year? Which you must if Daniel wasn't even deported until the third year of Jehoiakim's vassalship and thus not until the 7th year of Nebuchadnezzar.
You have to make special rulerships for both Nebuchadnezzar and Jehoiakim for this to work, when if you take this for FACE VALUE and accept that when the Bible says, "kingship" it means just that, and that when it says the second year of Nebuchadnezzar it means just that and just accept that Daniel was deported in the accession year of Nebuchadnezzar, which we know if it was near the end of the year, Nebuchadnezzar had become king by this time.
ACCEPT that when the Bible says that Jehoiachin was deported in the eighth year at the turn of the year, meaning the very end, that it means just that, not the 7th. The 7th year was the year Ezekiel was deported which matches his being in his 12th year when he heard that Jerusalem had fallen.
All this all amounts to is that the Bible's chronology was preserved correctly and that the Persians changed their records late in the reign of Darius II. That's all. The ancients changed their records ALL THE TIME when it was politically convenient or advantageous to do so.
Daniel says "kingship" for Jehoiakim's third year. I accept that for face value. Making it a vassalship means you have to change lots of other numbers. I can't accept your position to do so, just to try to agree with the WTS who happen to be wrong about this point. They are in "spiritual darkness" and this is part of the proof Jehovah has abandoned them. They are like the slave who was not watching and the thief comes in and steals his outer garments and now he is naked and exposed to shame.
You must leave them to have truth, Scholar! The truth is not with them. "Get out of Babylon the Great" or experience part of her plagues.
JC