So the apostates would argue that Daniel, as one of the “children” still learning the local language, had only been in the city several months before he was regarded as, not a child, but as an able-bodied man and one of the wise men of Babylon.
You should start basing your arguments on the original Hebrew/Aramaic words rather than their English translation. What is rendered as "children" in the NWT in Daniel 1:4, 17 is h-yldym which does not necessarily imply childhood but rather indicates that one is an "offspring" (cf. verb yld "to give birth, sire offspring"), and so it is used to refer to an adult Philistine soldier in 2 Samuel 21:20 (who was a "descendent of Rapha," or lit. "child of Rapha") and the Anakim in Numbers 13:28, and it overwise is typically used to refer to males from birth to marriageable age (Goldingay, p. 5). It thus is relevant to consider that the yldym in Daniel 1:4 refer to the "sons of Israel, the royal seed and the nobility" in the previous verse, i.e. they are royal and noble offspring. "Young men" would be a better translation than "children," and the curriculum of higher education being described in the verse was customary of males in the teens in the Persian court (cf. the otherwise Persian coloring of the story). The LXX renders yldym with the word neaniskous "young men", which is the word that occurs in 1 Esdras 3:4 to refer to the three young men in the court of King Darius.
I personally do not believe that ch. 2 is describing the same set of events as ch. 1 but for quite different reasons (i.e. ch. 2 has a different literary origin than ch. 1 and the tale is independent of the one in ch. 1). I'm surprised no one has mentioned the fact that the LXX of Daniel 2:1 places Nebuchadnezzar's dream in his twelfth year and that haplography may have caused the loss of the `shrh "ten" (since the eye can skip from shnt "year" to shtym "two"), or that the number could have been sht "six" and was substituted with the similar shtym "two".
I also do not regard Daniel 1 as reporting a tradition of a siege of Jerusalem in 605-604 BC (cf. Josephus, Antiquities 10.6.1), but rather represents a conflation between (1) the siege mentioned in 2 Kings 24:1-2 that occurred later in Jehoiakim's reign and (2) the siege of 597 BC that occurred during Jehoiachin's reign as described in 2 Kings 24:10-16. It was this later siege that carried off "the treasures of the Temple of Yahweh and the treasures of the royal palace," as well as "all the nobles and all the notables," which corresponds to the "the royal seed and the nobility" in Daniel 1:3. The author of the Hebrew apocalypse was induced to conflate the two events on the basis of the Chronicler, who had already duplicated the exile of Jehoiachin into an exile of Jehoiakim:
"Nebuchadnezzar king of Babylon had attacked him [Jehoiakim], loaded him up with chains and carried him off to Babylon. To Babylon Nebuchadnezzar also carried off part of the furnishings of the Temple of Yahweh and put them in his palace in Babylon ... the vessels of the Temple of Yahweh which Nebuchadnezzar had carried away from Jerusalem and placed in the temple of his god" (2 Chronicles 36:6-7, Ezra 1:7).
The author of Hebrew Daniel was literarily dependent on the Chronicler and shows verbatim agreement with his phrasing, showing that he is basing his account on the narrative of Jehoiakim's deportation in 2 Chronicles 36:
"Nebuchadnezzar king of Babylon marched on Jerusalem and besieged it. The Lord delivered Jehoiakim king of Judah into his hands, with part of the furnishings of the Temple of God. He took them away to the land of Shinar to the temple of his god, and placed the vessels of the house of God in the treasury of his god" (Daniel 1:1-2).
However 2 Kings 24 knows nothing of a deportation of Jehoiakim and even claims that he died in peace and "slept with his fathers" (v. 6), and the LXX of 2 Chronicles 36:8 claims that Jehoiakim was buried in the Garden of Uzzah in Jerusalem. More to the point, neither Ezekiel nor Jeremiah know anything about the king's exile, and Jeremiah 22:19 and 36:30 explicitly claims that Jehoiakim would die in disgrace in Jerusalem and have his dead body dragged out of the gates of the city (and neither did Jeremiah, who wrote into the reign of Zedekiah, correct this statement if Jehoiakim was in fact taken prisoner). Josephus (Antiquities 10.6.3) historicized this in a narrative about the siege of Jerusalem which he placed at the end of Jehoiakim's reign (cf. 2 Kings 24:1-2), claiming that Nebuchadnezzar ordered Jehoiakim's body be thrown outside of the walls of Jerusalem and "made his son Jehoiachin king of the country and the city". Since Jehoiachin ruled for only three months, and since Josephus described him as installed by Nebuchadnezzar, he apparently has merged the two sieges into a single event, such that the prophet Ezekiel was taken prisoner at the end of this siege and the figure Josephus gives for the number of captives is the one given in Jeremiah 52 for the number taken after 597 BC. But even this account stands in tension with the one in 2 Kings 24:6. And Josephus makes Daniel and his friends exiles taken in the final fall of Jerusalem at the end of Zedekiah's reign (cf. Antiquities, 10.10.1).
Further evidence of the conflation between Jehoiakim and Jehoiachin can be found in the fact that Ióakeim is the name given to both kings in 2 Kings 23-24 LXX, Matthew 1:11-12 also has Iekhonias (= Hebrew yknyh) as both the son of Josiah (i.e. Jehoiakim, cf. 2 Kings 23:34) and the father of Shealtiel (i.e. Jehoiachin, cf. 1 Chronicles 3:17), and the Jewish historian Eupolemus has combined the two kings into a single figure with the name Ionakhim (e.g. Jehoiakim + Jeconiah). Note also the thoroughgoing confusion of Hippolytus' account of the period:
"Now there are born to the blessed Josiah these five sons--Jehoahaz, Eliakim, Johanan, Zedekiah, and Jeconiah (cf. 1 Chronicles 3:16 in which Jeconiah is really the son of Jehoiakim), and Sadum. And on his father's death, Jehoahaz is anointed as king by the people at the age of twenty-three years. Against him comes up Pharaoh-Necho, in the third month of his reign; and he takes him (Jehoahaz) prisoner, and carries him into Egypt, and imposes tribute on the land to the extent of one hundred talents of silver and ten talents of gold. And in his stead he sets up his brother Eliakim as king over the land, whose name also he changed to Jehoiakim (cf. 2 Kings 23:34), and who was then eleven years old (cf. 2 Kings 23:36 in which he was 25 years old; his reign was eleven years). Against him came up Nebuchadnezzar king of Babylon, and carries him off prisoner to Babylon, taking with him also some of the vessels of the house in Jerusalem (cf. the exile of Jehoiakim in 2 Chronicles 36:6-7). Thrown into prison as a friend of Pharaoh, and as one set up by him over the kingdom, he is released at length in the thirty-seventh year by Evil-Merodach king of Babylon (cf. the release of Jehoiachin in 2 Kings 25:27); and he cut his hair short, and was counsellor to him, and ate at his table until the day that he died. On his removal, his son Jehoiakim reigns three years (note: the same name as the previous king). And against him came up Nebuchadnezzar, and transports him and ten thousand of the men of his people to Babylon, and sets up in his stead his father's brother, whose name he changed also to Zedekiah; and after making agreement with him by oath and treaty, he returns to Babylon. This (Zedekiah), after a reign of eleven years, revolted from him and went over to Pharaoh king of Egypt. And in the tenth year Nebuchadnezzar came against him from (he land of the Chaldeans, and surrounded the city with a stockade, and environed it all round, and completely shut it up" (Hippolytus, Commentary on Daniel, 1).
The exile alluded to in the beginning of Daniel thus probably reflects the events of the reign of Jehoiachin thrown back into the reign of Jehoiakim by the Chronicler, who also placed it at the terminus of Jehoiakim's reign (whereas 2 Kings does not date it and implies that Jehoiakim died in Jerusalem), allowing Josephus to combine the two sieges together into a single one (facilitated also by the brief reign of Jehoiachin), but in treating Jeremiah's datum about the death of Jehoiakim as historical he must sacrifice the claim by the Chronicler that Nebuchadnezzar took Jehoiakim prisoner back to Babylon. It's pretty difficult to assess what the actual history is but I suspect that Jehoiakim's exile is a duplicate of the one of Jehoiachin and the author of the Hebrew apocalypse was influenced by this.