Why did John the Baptist deny being an Elijah?

[Paidion]

Reincarnated or not, Jesus said that Elijah had already come. How else could He say that there was not going to be another fulfillment? Why say that he had already come if He expected Elijah to come again?

I have already addressed this question. Jesus said that John was Elijah to come because he fulfilled many of the prophecies which were predicted of Elijah. But, I suggest, He expected the actual Elijah to return at the appropriate time. Jesus Himself explained the two senses in which Elijah came and is to come in Matthew 17:10-12:

And the disciples asked him, “Then why do the scribes say that first Elijah must come?”
He answered, “Elijah is coming, and he will restore all things.

Jesus said, Elijah will (future to his time) restore all things. But John the Baptist had already been beheaded (Matthew 14:10), so how could He have been speaking of John the Baptist?

But I tell you that Elijah has already come, and they did not recognize him, but did to him whatever they pleased. So also the Son of Man will certainly suffer at their hands.”

So, having said that "Elijah is coming, and he will restore all things", which cannot apply to John the Baptist, Jesus then said that Elijah had already come in John the Baptist. John had come in the spirit and power of Elijah, and had fulfilled some of the prophecies concerning Elijah.

Exactly where would Elijah and Enoch exist while being preserved in their earthly bodies?

That question is not answered either in scripture or by the second-century writers. But God could preserve their bodies anywhere if He wished.

Would they be like the beloved disciple according to Mormon theology - still living somwhere (hiding out) awaiting the coming of the Lord (John 21:22)?

I have no reason to think they are hiding. Also, since they were both "taken" by God, I presume they do not live on earth.

They couldn't be in heaven in their physical body according to basic evangelical theology...

I don't put a whole lot of stock in basic evangelical theology.

...and according to what Jesus said in the first part of John 3:13.

Yes, the words of Jesus seems to contradict the idea that they went to heaven.