So after fishing about a bit online I came across a mehalach from Rabbi Pinchas Winston here - it seems to be based on the Arizal's Shaar HaGilgulim, Chapter 32 (translation can be found here). It is clearly, deeply kabbalstic, and I can't say I understand it totally, but it does somewhat help to unify all these disparate viewpoints.
Regarding Pinchas’ birth it says, “Elazar the son of Aharon took a daughter of Potiel for a wife and Pinchas was born” (Shemos 6:25). On this Chazal say: Potiel-this is Yosef, “sh’patpet” (controlled) his yetzer hara; this is Yisro, “sh’patem” (fattened) calves for idol worship. This is the sod: when Pinchas was born, he incorporated two soul-sparks. This is the meaning: “Potiel,” which is similar to “tippin” (drops), for he was from two soul-drops, one spark from the root of Yosef HaTzaddik and the second spark was from the side of Yisro. This level that incorporates these two souls is called “Pinchas.” (Sha’ar HaGilgulim, Chapter 32)
Thus, Pinchas was like a spiritual time bomb waiting to go off. Though he may not have been conscious of it himself, there was something in him waiting to burst forth when the time was right. All it would take was the proper ignition, and then the two soul-sparks that Pinchas contained would reveal themselves through his act of zealousness......
... The soul that comes to a man when he is born is an actual gilgul, even if it is the combination of two sparks, as in the case of Pinchas who had a spark of Yosef and a spark from Yisro. Nothing else is required to coalesce them. (Ibid.)
In other words, they automatically join with the body and remain with it until the person dies; the body cannot survive without them, and they cannot leave the body before its time is up. However:
In the case of a soul that comes b’sod ibur after birth, like the Nefesh of Nadav and Avihu that came to Pinchas, another spark must accompany it. Furthermore, this spark must be new to the world and not a reincarnation. Such a spark joined with the Nefesh of Nadav and Avihu that came b’ibur, to unify it with the Nefesh of Pinchas, which was an actual reincarnation. Therefore, another new soul had to come b’ibur in Pinchas called “Eliyahu HaTishbi” from the inhabitants of Gilad, and from the root of Gad, which was a new soul at that time. This was in order to combine the Nefesh of Nadav and Avihu with the Nefesh of Pinchas itself, a gilgul from the time of his birth. (Ibid.)
Thus, reviewing the composition of Pinchas’ soul, we find that he was born with a soul-spark from both Yosef HaTzaddik and Yisro, Moshe’s father-in-law. This was the soul with which he was born, and which made him Pinchas ben Elazar HaKohen, and with which he would have died, had he not metamorphosed into a new being called “Eliyahu HaNavi.”
However, when he acted zealously by killing Zimri and Cozbi in last week’s parshah, he inherited two additional souls, that of Nadav and Avihu, which, apparently, had been on a long journey through history in the process of tikun. Since these were not Pinchas’ main souls, they could come and go as was necessary, enhancing Pinchas’ spiritual ability, and therefore required something to “bind” them to him. That extra soul is called, “Eliyahu HaTishbi” from the root of Gad.
Thus, Eliyahu who never died, but had ascended to Heaven in a fiery chariot to become an angel, had not been born either. He was a soul that entered and attached itself to an existing person, Pinchas ben Elazar.
And, as if that wasn’t confusing enough, the Arizal explained further:
He also required an additional new soul in order to unite the new soul called “Eliyahu HaTishbi” with the rest of the older souls, that is, the Nefesh of Pinchas and that of Nadav and Avihu. Therefore, he received an additional soul called “Eliyahu” from the root of Binyomin, mentioned in Divrei HaYomim in the posuk, “And Ya’areshyah, Eliyahu, and Zichri were the sons of Yerucham” (I Divrei HaYomim 8:27), as Eliyahu himself wrote to the Chachamim, “from the children of the children of Rachel” (Bereishis Rabbah 71:12) . . . Thus we find that four levels were in Pinchas. The first was that of the Nefesh of Pinchas with which he was born, a single soul even though it was the combination of two drops, one from Yosef and one from Yisro. The second level was the Nefesh of Nadav and Avihu, which came b’sod ibur and was also called “one soul,” as is known from the Zohar: Nadav and Avihu were two limbs of one body (Acharei Mos 57b). The third was a Nefesh called “Eliyahu HaTishbi” from the root of Gad, and the fourth level was “Eliyahu” from the root of Binyomin. (Ibid.)
