You ask whether the following, admittedly mysterious, passage “implies a doctrine of reincarnation”:
“And as they departed, Jesus began to say unto the multitudes concerning John…. This is he, of whom it is written, Behold, I send my messenger before thy face, which shall prepare thy way before thee. Verily I say unto you, Among them that are born of women there hath not risen a greater than John the Baptist: notwithstanding he that is least in the kingdom of heaven is greater than he…. And if ye will receive it, this is Elias, which was for to come” (Matt. 11:7-14).
It’s certainly common enough for theosophists and other “new age” interpreters to see some sort of equation here—John = Elias—and to account for it in terms of palingenesis. I would be most cautious, however, in adopting this all-too-horizontal interpretation, not least because the Baptist himself rejects it (John 1:21). And for good reason: if he and Elias are one and the same, how are we supposed to explain the appearance of Elias—qua Elias, not John—on Mount Tabor (Matt. 17:1-9) after John’s own gruesome death (Matt. 14:1-12)? Would we then be obliged to posit a case not of re- but of retro- incarnation?!
A much wiser approach to the subject is outlined by the perennialist author Leo Schaya, in an article whose title is itself the key: “The Eliatic Function“. I recommend the whole piece but would call your attention here to the following decisive passage:
“One aspect peculiar to the universal function of Elias resides in the fact that this function can be exercised by others than Elias…. Elias … means not only a prophet sent to Israel, but also a universal function which may be exercised by several people, both within Judaism and within other traditions, and whatever be the names given by these traditions to the unique celestial source of this descent of the “Spirit which bloweth where it listeth”. The possibility of his multiple personification is made evident in the Gospel, which identifies John the Baptist with him who “crieth in the wilderness and prepareth the way of the Lord” (Matt. 3:3; Luke 3: 4-6; John 1:23). He who is thus denoted first by Isaiah (40:3) is—according to Jewish tradition—the precursor of the Messiah, the immortal prophet Elias. John the Baptist refused to be confused with him; however, he affirmed that he was the one of whom Isaiah spoke, and by this apparent contradiction he made it quite evident that, without being Elias in person, he exercised in his own time and orbit the Eliatic function.”
Something tells me you’re not going to be satisfied with this explanation, however. It’s hard to hear the “tone” in an email, but I have the impression this is for you a more than academic question. On the contrary, you seem to be on something of a mission to find a Biblical basis, however tenuous, for a doctrine that you, as a Christian, are already predisposed to believe in. I won’t try to argue you out of this stance—predispositions seldom yield to argument anyway—though I would like to warn you against invoking perennialism as a justification for your mission. One can’t say it often enough, it seems: The unity of the great traditions is transcendent and “stratospheric”, not immanent or “atmospheric”, which means in this case that we must steer clear of all mixing and matching of eschatologies. Is there any truth to the doctrine of reincarnation? Of course. But it’s not a truth, or form of the Truth, that a Christian qua Christian needs, and attempts to graft it onto a Christian branch will not produce the fruit you suppose.
And even supposing they could, so what? Eschatology—like cosmology—is a derivative, second-order science. Its particulars are indications and pointers, not one-for-one mappings, and what they point us toward is a State in which considerations of post-mortem states are no longer of consequence. The following from Wolfgang Smith’s Christian Gnosis: From Saint Paul to Meister Eckhart may help you to grasp what I’m saying. I recommend meditating with particular care on what Smith calls “the standpoint Eckhart has made his own”:
“The question now obtrudes whether indeed every Christian is called to gnosis, or better said: whether salvation and supreme gnosis are, after all, one and the same. Might there not be ‘lesser’ stations in the Kingdom of God, in accordance with the words ‘in my Father’s house there are many mansions’? Or are we to think, perhaps, that the ‘way’ normally continues after death: that to attain its true end, the soul is generally obliged to pass through a series of post-mortem states culminating at last in the realization of gnosis (in keeping with the Vedantic notion of krama mukti or ‘gradual liberation’)? Is this, perhaps, the explicated sense of what the Church terms Purgatory?
It appears that these are matters Eckhart does not discuss, does not consider at all. They are questions, moreover, posed from a ‘creaturely’ point of view, which disappear from the standpoint Eckhart has made his own: where ‘all creatures are one pure nothing’, what is there to be said concerning ‘heavens’ and ‘hells’? One is reminded of a Vedantic text which speaks to this issue in what might be characterized as ‘initiatic’ terms, evidently designed to arouse the disciple from his ‘theological slumbers’: ‘There is neither dissolution nor genesis, none in bondage and none practicing [yogic] disciplines. There is no one seeking liberation and no one liberated. This is the final truth.'”