John 3:13 And no man hath ascended up to heaven, but he that came down from heaven, even the Son of man which is in heaven.Rather than speculate the plain teaching of Elijah's translation is incorrect, its better to admit nothing in Elijah's Letter (2 Chron. 21:12-15) proves Elijah wasn't translated to heaven.
He could have penned it in heaven and angels delivered it:
Do not forget to entertain strangers, for by so doing some have unwittingly entertained angels. (Heb. 13:2 NKJ)
You cited the Jewish Encyclopedia, but better than them are Keil and Delitzsch who, after looking at all the facts, conclude no one can say Elijah was not translated into heaven. Only that Lightfoot's proof he was isn't that strong. I, on the other hand, thought it quite strong, just not a smoking gun.
In regard to this statement, we need not be surprised that nothing is elsewhere told us of any written prophecies of Elijah; for we have no circumstantial accounts of his prophetic activity, by which we might estimate the circumstances which may have induced him in this particular instance to commit his prophecy to writing. But, on the other hand, it is very questionable if Elijah was still alive in the reign of Joram of Judah. His translation to heaven is narrated in 2 Kings 2, between the reign of Ahaziah and Joram of Israel, but the year of the event is nowhere stated in Scripture. In the Jewish Chronicle Seder olam, 2 Chron. 22:1, it is indeed placed in the second year of Ahaziah of Israel; but this statement is not founded upon historical tradition, but is a mere deduction from the fact that his translation is narrated in 2 Kings 2 immediately after Ahaziah’s death; and the last act of Elijah of which we have any record (2 Kings 1) falls in the second year of that king. Lightfoot, indeed (Opp. i. p. 85), Ramb., and Dereser have concluded from 2 Kings 3:11 that Elijah was taken away from the earth in the reign of Jehoshaphat, because according to that passage, in the campaign against the Moabites, undertaken in company with Joram of Israel, Jehoshaphat inquired for a prophet, and received the answer that Elisha was there, who had poured water upon the hands of Elijah. But the only conclusion to be drawn from that is, that in the camp, or near it, was Elisha, Elijah’s servant, not that Elijah was no longer upon earth.
Keil, C. F., & Delitzsch, F. (1996). Commentary on the Old Testament (Vol. 3, p. 643). Hendrickson.
You said: He could have penned it in heaven and angels delivered it:
That is only an assumption on your part as according to John 3:13 no one has ever ascended up to heaven other that Jesus.
There came writing to Jehoram from Elijah the prophet, saying..." (2Chron 21:12). Now the wickedness of Jehoram, for which he was being rebuked in the letter, took place after Elijah was taken away, yet the letter speaks of these things as past events, and the punishment to come upon him as yet future. So the idea of some, that Elijah wrote the letter before he was removed by the whirlwind, is proved wrong.
Elijah was taken up by the whirlwind into the first heaven and transported to another location on Earth. God did not see fit in His purpose to reveal his whereabouts. Chariot of fire is used at times figuratively for host (angels) like in 2 Kings 2:11, 12: 6:17; Psalms 68:17; 104:1-4. Elijah, by his prayers and his counsel was the "chariot of Israel and the horseman thereof", meaning Elijah was the stronghold of Israel, the driving force of God. The Israelite's never used chariots till the time of David.
When you compare 2 Kings 2:11-15 with 2 Kings 6:17 you see that God sent the host/angels down to Elijah who caught him up in a whirlwind and translated him to parts unknown. Several years after he was taken away King Jehoram received a letter from him.
What some people do not know is that there are three heavens. The first heaven is the Atmosphere, the air surrounding the earth. Birds fly "in the heaven" - certainly not to God's throne. We read in Genesis l:2 of "foul that may fly above the Earth in the open firmament of heaven." Jacob, when blessing Isaac, said: "God give you of the dew of heaven," and Moses was joyful that the "heavens shall drop down dew" (Gen.27:28; Deut.33:28). The dew comes from the first heaven - the atmosphere. The second heaven is the expanse of this awesome universe - where the stars, moon and planets are. The Psalmists often wrote about the "Heavens, the work of your fingers, the moon, and the stars, which you have ordained" (Ps.8:3; Gen.1:15-17). The third heaven is where the throne of God exists, where the heavenly temple is found and the heavenly Jerusalem.
2 Chronicles Chapter 21 - Jehoram, being the son of Jehoshaphat, was 32 when he began his reign in Israel. He married Ahab's daughter and was a wicked king who reigned for eight years. According to scripture Elijah was taken up in a whirlwind, 2 Kings 2:11-13. The heaven Elijah went up to was only the first heaven being the atmosphere as there are three heavens described in scripture as the throne of God is in the third heaven. A whirlwind can only happen within the atmosphere of the first heaven. During the reign of Jehoram he received a letter from Elijah, 2 Chronicles 21:12-15. How could he receive a letter from Elijah if he was with God in the third heaven? Elijah being caught up to heaven is the same as Phillip being caught up in the first heaven and carried thirty miles away, Acts 8:39, 40. The only difference is that when the fifty men searched for Elijah they could not find him as he was translated further than their search. Phillip was found within the thirty mile radius where he was translated to.