This is a very interesting thread. I myself am currently studying up on ancient semetic religious beliefes as well as babylonian, persian and hindu doctrines.
First of all, I am a Member of the Church of Jesus Christ of Latter Day Saints, so this should belay my bias upfront.
I have an intersting hypothesis as to who Melchezedek was/is. As I believe that Melchezedek was translated (ascended to heaven without dying) I do not believe he could have been Shem, as I am under the impression that he did actually die. A also do not believe in reincarnation or that God the father would have come directly to Earth (as the scriptures show that God typically sends messengers in his place, with very few exceptions) specificaly to have Avrahim to pay tithes to him and show him the sacrament. Avrahim also shows no inclination to say that Melchezedek was anything more than an extremly righteous high priest of God, in other words, he was definitely a man, albeit a near perfect man
The fact that he is not mentioned to have a lineage though can be for several reasons. One possibility being that it was intentionaly left out.
Here is where my LDS bias comes in.
I would like to point out, that for many decades now, there have been many Theologins and Scholars that have tried to say that Judaism, Christianity and Islam have stolen/adopted many beliefes from a little known world religion (at least, it could be considered a world religion in its hay day) called Zorastrianism (not to be confused with the cult of Mithras, which was a heresy under Zorastrianism).
These scholars may have actually have been on to something, in a way at least.
First let me give some background knowledge and conjecture.
I will start at the time of Jesus. We all know who the Pharisees and the Saducees were, but there was also a group called the Essenes/Hasidim as well. The word Pharisee originates as the word Pharis, which is the Aramaic term for "of Pharis/Persia". In other words, the Pharisee were a sect of Judaism from persia. The pharisee believed in the ressurection, a judgement of the soul, and in the angels of heaven. The Saducees however, did not, they only believed in the most literal interpretation of the books of moses, which makes no mention of angels, heaven, a hell or anything of that sort. The essenes did believe in much of what the pharisees did as well, but with some twists and extremes.
I would like to point out that the saducees were not incorrect in their beliefes as they were going dirctly upon what the LORD had given them. So then why did the Essenes and the Pharisees differ from them?
So here is some info on the Zorastrin/Mhazdaist religious beliefes, and the LDS members reading this can confirm this through the LDS institute of religions book of world religions (not the actual title) as well as a 1971 general conference talk (easily found in the Ensign archives) given on the faith.
The date of origin for the faith is highly contested. The adherents, as well as the writings of Plato, place the faiths start date in the year we would consider to be around 6000 bc. Many scholars scoff at this record and instead claim that it was a misprint and what Plato meant to say was essentially 600 bc. Since that point, 600 bc became the widely accepted view of its origin.
However, current studies of the linguistics used in this faiths oldest surviving text denotes a date of at least 1500-1300 bc. Which makes the origin of the faith at least 700 years older than the “scholars” said it was.
It began when a man, by the name of Zarathushtra (greek; Zoraster, Egyptian; Zorokothora, Parsean; Zartoshtra), seeks out spiritual enlightenment, by fasting on and off for thirty or so years and doing a lot of praying, in what we would now call bactria afganistan. He goes through a ritualistic cleansing and bathing in a local holy river, while he is doing this, he is visited by an angel, the angel tells him that he is the servant of Ahura Mhazda (farsi for Lord of Wisdom). He is then taken up and shown many visions of heaven and given many rules that man should live by.
In Zarathushtras day, his people worshipped a pantheon of deities called Daeva. When he receives his enlightenment from the One True God (Ahura Mhazda) he is told that the Daeva should not be worshipped because they are evil malighned beings trying to make man chose evil deeds and thoughts over good ones. This is, etymologically speaking, where we get the word Devil.
In fact, a villain is revealed to Zarathustra by the name of Angra Mainyu (Evil/Angry Spirit) who is Ahura Mhazdas chief adversary, he even goes so far as to give a title very familiar to madern day Christians, the title being “The Prince of Lies”.
Zarathushtra, being called of this deity as a prophet, goes on to preach this new religion with little success until he becomes sanctioned by a king. Later, the religion becomes the primary religion of Persia through the act of proselytization, as he establishes a priesthood via the converts of former Daeva priests who converted to the knew religion, these preists are then sent throughout the known world, there is evidence that the religion reached as far as present day Armenia (as the primary deity of worship in pegan Armenian religion goes by the name of Ormazd).
Primary key tenants of this religion are
1. Belief in a singular God, who has an adversary that has existed as long as he has.
2. Belief of Yazatas (Angels) as guardians of man and messengers of God (EDIT NOTE: All Zorastrian Angels were mentioned by SPECIFIC names, usually denoted by the Job they performed)
3. Belief that the Soul and Body would be reunited (The resurrection) at the final renovation (judgement) of the world
4. A belief in a Paradisae, used with the symbolism of the sun for the most righteous who practice Good Thoughts, Good Words and Good Deeds
5. Those who do not quite make it to this heaven, will enter into one of three degrees of damnation, likened unto the moon, the stars and a place completely devoid of light.
6. A strong belief in eternal marriage is also posited amongst this religion. But only those marriages performed by the priests in the fire temple were counted as eternal.
7. Finaly, a belief in a Saiyoshyant (Mesiah/Savior) would come to the earth and purify man (although, depending on the period in this faith, they have been known to believe in up to 3 saviors)
Zarathushtra also taught that blood sacrifice was to be stopped, as he himself abhorred the practice, and instituted a tithe system in its place. He also preached against the use of opiates and mind altering substances such as Haoma drink (druged wine, closest English description) in priestly ceremonies.
Many of the traditions of this religion also teach that Zarathushtra did not die, but was, in fact, lifted up to heaven. However, there are also others that say he was killed, and some claim he died peacefully at 77.
This religion, assuming the date of the origin of this faith is at least at 1300 bc, would be the first to teach of angels and the resurrection, a heavenly paradise and a concept of hell very dissimilar to the oblivion afterlives of the Greeks and Babylonians.
Ok, so here is the connection, none of the above doctrines were present in Jewish scripture (EDIT NOTE: in regards to NAMED angels, the hebrew faith did not write down the names of angels until the occupation, as the name was seen as sacred much as the name of God/Yavhevavhe/Yahwe was writting as LORD/Adoni) until the Persian occupation of Israel. And later, these doctrine become enforced by Jesus, with the perceived exception of eternal marriage, when He is asked by the Pharisee as to which man would have a particular woman in the afterlife as she was widowed and remarried, Jesus said neither, not because there is no eternal marriage but because either, she or the men were not living a celestial marriage.
Jesus makes the claim that his priesthood order is after the order of Melchezedek. And the doctrine he enforces is Persian in its origin. But even still, later in Gnostic scripture known as the Pistis Sophia, Jesus teaches the Apostles about Zorokothora Melchezedek and the mysteries of God through the use of his priesthood.
So here is the hypothesis, what if Zarathustra was Melchezedek?
As we currently believe that Avrahim existed around 1800 bc, it is not to much of a stretch to say that the Mhazdaist faith may have also existed at the same time as the OLDest SURVIVING document of Zarathushtras Gathas purport back to at least 1300-1500 bc.
what if Melchezedeks lineage was left out becuase he was actually a foreigner and no one really knew?
The life story of Zarathustra is also somewhat, very tentatively, reinforced by what Alma says about Melchezedek in the Book of Mormon
Alma's sermon in chapters 12 and 13 teaches the principle that God will provide men access to certain mysteries of God (Alma 12:9—11). The first verse of this sermon sets the theme for the entire discourse. Alma says that many know these mysteries as priests (Alma 13:1), but they are laid under a strict condition of secrecy (Alma 12:9) that can be lifted only by the diligence and repentance of the children of men (Alma 12:9—11; 13:18; cf. Alma 26:22). The plan provides all mankind a chance to know the mysteries in full (Alma 12:10), by humility (Alma 12:10—11; 13:13—14) and through the ministrations of properly ordained priests (Alma 13:16; cf. Mosiah 2:9; Alma 26:22) (John W. Welch: "The Melchizedek Material in Alma 13:13-19"
, for more info on churches view of Melchezedek).
The similarity being the humility and pious search for truth that the Mhazdaists believe Zarathustra went through, and that Alma obviously believed that Melchezedek went through.
Yes, I know this is all speculation, and moderate portion of this ‘evidence’ is highly circumstantial. But very fun none the less.