I was reading through the Anchor Bible Dictionary (got it for Christmas) and found a few things I'd never noticed before. Like, John the Baptist denying that he's Elijah but Jesus saying that he is (John 1:21 vs. Matthew 17:9-13). So, I did a little more research using Thomas Aquinas' "Catena Aurea" (Golden Chain) and flipping through the cross-references in my bible.
Thomas attributes the following to "Gregory" (meaning St. Gregory of Nyssa, St. Gregory of Nazianzus, or Pope Gregory I (the Great)). If I did some more research, I could probably tell you which one but it's just abbreviated in this book and I don't see a table of abbreviations.
The angel tells Zacharias concerning John, He shall go before Him in the spirit and power of Elias (Luke 1:17). As Elias then will preach the second advent of our Lord, so John preached his first; as the former will come as the precursor of the Judge, so the latter was made the precursor of the Redeemer. John was Elias in spirit, not in person : and what our Lord affirms of the spirit, John denies of the person : there being a kind of propriety in this; viz. that our Lord to His disciples should speak spiritually of John, and that John, in answering the carnal multitude, should speak of his body, not of his spirit.
Origen echoes something similar.
But perhaps, since Elias was expected to appear before the coming of Christ near the end, they may seem to put the question figuratively, Art thou he who announcest the coming of Christ at the end of the world? to which he answers, I am not.
So it seems a Orthodox/Catholic response to the difference between John and Matthew on whether or not John the Baptist is Elijah would be that John the Baptist foreshadows what Elijah will when Christ comes again to judge humanity at the end of time. John the Baptist is like Elijah in that he does things that Elijah will also do. But John the Baptist isn't Elijah. He's John.
But does this explanation hold any weight? A pertinent passage about Elijah (that my Bible pointed me to) is in Malachi 4:5-6.
Behold, I will send you Elijah the prophet before the coming of the great and dreadful day of the LORD: And he shall turn the heart of the fathers to the children, and the heart of the children to their fathers, lest I come and smith the earth with a curse.
Sounds pretty apocalyptic to me, but it also cross-references Joel 2:31 here for good measure.
The sun shall be turned into darkness, and the moon into blood, before the great and the terrible day of the LORD come.
So it seems consistent with the notion that John probably isn't Elijah and doesn't have to be Elijah. But is it consistent with Matthew 17:11-13?
And Jesus answered and said unto them, Elias truly shall first come, and restore all things. But I say unto you, That Elias is come already, and they knew him not, but have done unto him whatsoever they listed. Likewise shall also the Son of man suffer of them. Then the disciples understood that he spake unto them of John the Baptist.
Seems to me there's still something unsettling there. So I went back to the Catena Aurea and looked up what early fathers had to say about this passage. St. John Chrysostom cleans things up relatively nicely.
The disciples knew not of the coming of Elias out of the Scriptures; but the Scribes made it known to them; and this report was current among the ignorant multitude, as was that concerning Christ. Yet the Scribes did not explain the coming of Christ and of Elias, as they ought to have done. For the Scriptures speak of two comings of Christ; that which has taken place, and that which is yet to be. But the Scribes, blinding the people, spake to them only of His second coming, and said, If this be the Christ, then should Elias have come before Him. Christ thus resolves the difficulty, He answered and said, Elias truly shall come, and restore all things; but I say unto ou, that Elias has already come. Think not that here is a contradiction in His speech, if He first say that Elias shall come, and then that he is come. For when he says that Elias shall come and restore all things, He speaks of Elias himself in his own proper person, who indeedshall restore all things...
...when He says that Elias is come already, He calls John the Baptist Elias from the resemblance of their ministry; for as Elias shall be the forerunner of His second coming, so was John the forerunner of His first. And He calls John Elias to shew that His first oming was agreeable to the Old Testament, and to prophecy.
There are still some loose ends lying around here and there, I think. I never thought that 30 mins of research would present an exhaustive answer, but it did provide a relatively satisfactory one -- especially since Jesus tends to speak in puzzling ways.