Stop embarrassing yourself!
Incarnation which literally means embodied in flesh or taking on flesh, refers to the conception and birth of a sentient creature (generally a human) who is the material manifestation of an entity, god or force whose original nature is immaterial.
Reincarnation (literally, "to be made flesh again"): believed to occur when the soul or spirit, after death of the body, comes back to Earth in another body.
Neither Jesus nor the angel said that John the Baptist and Elijah were the same person.
Luke 1:17
17And he will go on before the Lord, in the spirit and power of Elijah, to turn the hearts of the fathers to their children and the disobedient to the wisdom of the righteous—to make ready a people prepared for the Lord."
Matthew 11:14
And if you are willing to accept it, he is the Elijah who was to come.
Okay...
Let's assume for a minute that I concede your assertion regarding Elijah... let's accept your newly tweaked translations of those passages and let's just forget that billions of Christians believed John the Baptist to be Elijah reincarnated/returned for two thousand years...
Let's just concede all of that for the sake of argument...
That still leaves 100,000,000,007 instances of reincarnation in the Bible...? Doesn't it?
The Luke