Is Matthew’s genealogy missing a person?

So all the generations from Abraham to David are fourteen generations, from David until the captivity in Babylon are fourteen generations, and from the captivity in Babylon until the Christ are fourteen generations. Mt. 1:17

This verse has become the basis for some controversy over the past 1600 years as students of Scripture counted the names in the preceding genealogy and invariably came up with thirteen names in the final set. That is, they numbered it like this: After the deportation to Babylon, Jeconiah begot Shealtiel (1), Shealtiel begot Zerubbabel (2), Zerubbabel begot Abiud (3), Abiud begot Eliakim (4), and Eliakim begot Azor (5). 14 Azor begot Zadok (6), Zadok begot Achim (7), and Achim begot Eliud (8). 15 Eliud begot Eleazar (9), Eleazar begot Matthan (10), and Matthan begot Jacob (11). 16 And Jacob begot Joseph the husband of Mary (12), of whom was born Jesus who is called Christ (13).
Scandalous! What has become of our fourteenth generation? Theological liberals have used this as proof of the corruption of the Scripture. More orthodox figures have proposed various explanations. Frederic Spanheim Sr., in his work Dubia Evangelica, surveys the different proposals in Dubium XVI. They are as follows:

1. Theophylact: the deportation to Babylon is to be counted as a person.
2. Augustine lib. II de Cons. Evang. cap. 4: Jeconiah should be numbered twice. Once at the end of the second set of fourteen, and once at the beginning of the third, on account of his two-fold condition, of a king and then private person, the former before the deportation and the latter after.
3. Others: David, rather, should be counted twice, at the end of the first as a private man, and at the beginning of the second as king, and Jeconiah should thus be referred to the third set of fourteen.
4. Yet others: Josiah should be counted twice, at the end of the second and the beginning of the third.
5. Epiphanius, lib. I adv. Haer. Haer. 8. A generation was lost in the transmission of the gospel of Matthew. This is the opinion of Maldonatus, Epiphanius, Ambrose, Euthymius, and others.
6. Ludovicus de Dieu: The virgin Mary gets her own generation, so that Jacob -> Joseph is the twelfth, Joseph -> Mary the thirteenth, and Mary -> Jesus the fourteenth.
7. The name Abner should be present between Abiud and Eliakim in v. 13.
8. Spanheim’s own view, and that of Jerome[1]: there are two historical Jeconiahs, the first the son of Josiah, and the second the father of Shealtiel, and their names are spelled differently in the Hebrew, and only come to appear alike through their transliteration to Greek. Therefore, Jeconiah should be counted twice, since there are in fact two Jeconiahs.

Which of these is correct? Two notes. First, one must count inclusively. Like how Christ died on a Friday and rose on a Sunday, and that is counted as three days because people in those days counted days inclusively, without concern for a whole 24 hours having passed for each day counted, so the generations of Matthew are numbered inclusively. This is, the names are numbered, not the spans. It is not Abraham -> Isaac (1), but Abraham (1) -> Isaac (2). Secondly, the assertion of Spanheim and Jerome that there are two Jeconiahs is well supported by Scripture. In 2 Chronicles 36 we read the following:

v. 4 Then the king of Egypt made Jehoahaz’s brother Eliakim king over Judah and Jerusalem, and changed his name to Jehoiakim.

And in v. 8, we read,
Now the rest of the acts of Jehoiakim, the abominations which he did, and what was found against him, indeed they are written in the book of the kings of Israel and Judah. Then Jehoiachin his son reigned in his place.

How did these names come to be equivalent? Jerome says through a transmission error; Spanheim, ever the believer in the pure transmission of Scripture, believes it was Matthew’s own decision.

The numbering, therefore, should be as follows:

v. 2 Abraham (1) begot Isaac (2), Isaac (2) begot Jacob (3), and Jacob (3) begot Judah (4) and his brothers. 3 Judah (4) begot Perez (5) and Zerah by Tamar, Perez (5) begot Hezron (6), and Hezron (6) begot Ram (7). 4 Ram (7) begot Amminadab (8), Amminadab (8) begot Nahshon (9), and Nahshon (9) begot Salmon (10). 5 Salmon (10) begot Boaz (11) by Rahab, Boaz (11) begot Obed (12) by Ruth, Obed (12) begot Jesse (13), 6 and Jesse (13) begot David the king (14).

David the king (14) begot Solomon (1) by her [b]who had been the wife of Uriah. 7 Solomon (1) begot Rehoboam (2), Rehoboam (2) begot Abijah (3), and Abijah (3) begot [c]Asa (4). 8 Asa (4) begot Jehoshaphat (5), Jehoshaphat (5) begot Joram (6), and Joram (6) begot Uzziah (7). 9 Uzziah (7) begot Jotham (8), Jotham (8) begot Ahaz (9), and Ahaz (9) begot Hezekiah (10). 10 Hezekiah (10) begot Manasseh (11), Manasseh (11) begot [d]Amon (12), and Amon (12) begot Josiah (13). 11 Josiah begot [e]Jeconiah (14) and his brothers about the time they were carried away to Babylon.

12 And after they were brought to Babylon, Jeconiah (1) begot Shealtiel (2), and Shealtiel (2) begot Zerubbabel (3). 13 Zerubbabel (3) begot Abiud (4), Abiud (4) begot Eliakim (5), and Eliakim (5) begot Azor (6). 14 Azor (6) begot Zadok (7), Zadok (7) begot Achim (8), and Achim (8) begot Eliud (9). 15 Eliud (9) begot Eleazar (10), Eleazar (10) begot Matthan (11), and Matthan (11) begot Jacob (12). 16 And Jacob (12) begot Joseph (13) the husband of Mary, of whom was born Jesus who is called Christ (14).17 So all the generations from Abraham to David are fourteen generations, from David until the captivity in Babylon are fourteen generations, and from the captivity in Babylon until the Christ are fourteen generations.

[1] For the citation from Jerome, see Migne’s Patrologia Latina v. 26 p. 23 footnote 2.