When an Old Testament saint died he went to paradise, or Abraham's bosom. He could not go to heaven because his sins had only been remitted, not redeemed. My question: What about Enoch and Elijah?

I am one of the teachers who believes that the Old Testament saints were transferred from the heart of the earth to heaven after the resurrection Christ. The argument goes like this:

1. In the story of the rich man and Lazarus, Abraham's bosom, the place where Lazarus was comforted, was directly next to hell (Luke 16:22-26 [22] And it came to pass, that the beggar died, and was carried by the angels into Abraham's bosom: the rich man also died, and was buried; [23] And in hell he lift up his eyes, being in torments, and seeth Abraham afar off, and Lazarus in his bosom. [24] And he cried and said, Father Abraham, have mercy on me, and send Lazarus, that he may dip the tip of his finger in water, and cool my tongue; for I am tormented in this flame. [25] But Abraham said, Son, remember that thou in thy lifetime receivedst thy good things, and likewise Lazarus evil things: but now he is comforted, and thou art tormented. [26] And beside all this, between us and you there is a great gulf fixed: so that they which would pass from hence to you cannot; neither can they pass to us, that would come from thence.
   See All...).
2. Hell is connected with the direction of down in the Bible (Psalm 55:15Let death seize upon them, and let them go down quick into hell: for wickedness is in their dwellings, and among them.
   See All...; Isaiah 14:15Yet thou shalt be brought down to hell, to the sides of the pit.
   See All...; Matthew 11:23And thou, Capernaum, which art exalted unto heaven, shalt be brought down to hell: for if the mighty works, which have been done in thee, had been done in Sodom, it would have remained until this day.
   See All...). Jesus spoke of going to the "heart of the earth" for three days and nights (Matthew 12:40For as Jonas was three days and three nights in the whale's belly; so shall the Son of man be three days and three nights in the heart of the earth.
   See All...) and also speaks of being in "paradise" (Luke 23:43And Jesus said unto him, Verily I say unto thee, To day shalt thou be with me in paradise.
   See All...) during this time (which would  match Abraham's bosom and is next to hell). Evidently, hell is in the center of the earth as was paradise, or Abraham's bosom, in earlier times.
3. The Bible refers to Jesus leading captivity captive when He ascended on high (Ephesians 4:8Wherefore he saith, When he ascended up on high, he led captivity captive, and gave gifts unto men.
   See All...). Paul connects paradise with the third heaven in 2 Corinthians 12:2-4 [2] I knew a man in Christ above fourteen years ago, (whether in the body, I cannot tell; or whether out of the body, I cannot tell: God knoweth;) such an one caught up to the third heaven. [3] And I knew such a man, (whether in the body, or out of the body, I cannot tell: God knoweth;) [4] How that he was caught up into paradise, and heard unspeakable words, which it is not lawful for a man to utter.
   See All.... These and other verses lead us to believe that the Old Testament saints were transported to heaven at the time of the ascension of Christ.
4. The speculated reason for this transfer is that the blood of Christ had not yet been applied to the Old Testament saints since Jesus had not yet died. We know that their full redemption awaited the death and resurrection of Christ. He "is the mediator of the new testament, that by means of death, for the redemption of the transgressions that were under the first testament, they which are called might receive the promise of eternal inheritance" (Hebrews 9:15And for this cause he is the mediator of the new testament, that by means of death, for the redemption of the transgressions that were under the first testament, they which are called might receive the promise of eternal inheritance.
   See All...). It makes sense that their entrance into heaven was not realized until the blood of the Lamb was shed and applied to their souls.

However, as you note, there seem to be exceptions in the case of Enoch and Elijah who were translated into heaven. Moses, who was evidently resurrected before the death of Christ, also presents a problem. I do not have an absolute answer, but I would like to make some observations:

1. It is only speculation that the saints had to wait for the shed blood of Christ before they could enter heaven. It makes sense to me, but there is no direct statement of scripture that says this is the case. There could be other reasons for their wait as well.
2. We say that no defiled thing can enter heaven. This is certainly true of the New Jerusalem (Revelation 21:27And there shall in no wise enter into it any thing that defileth, neither whatsoever worketh abomination, or maketh a lie: but they which are written in the Lamb's book of life.
   See All...) and one would think it true of the heavenly temple. However, Satan has access to some level of heaven as we see in Job 1:6Now there was a day when the sons of God came to present themselves before the LORD, and Satan came also among them.
   See All.... Surely, nothing is more defiled than he is.
3. God practices levels of access in the design of the earthly tabernacle and temple, with different levels of access in the courtyard, the main tabernacle, and the holy of holies. Perhaps He has levels of access in heaven as well.
4. And, despite what our doctrinal logic tells us, scripture tells us that Enoch "was not; for God took him" (Genesis 5:24And Enoch walked with God: and he was not; for God took him.
   See All...) and "was translated that he should not see death" (Hebrews 11:5By faith Enoch was translated that he should not see death; and was not found, because God had translated him: for before his translation he had this testimony, that he pleased God.
   See All...). It also tells us that "Elijah went up by a whirlwind into heaven" (2 Kings 2:11And it came to pass, as they still went on, and talked, that, behold, there appeared a chariot of fire, and horses of fire, and parted them both asunder; and Elijah went up by a whirlwind into heaven.
   See All...). God clearly gave them a special privilege and portion. Just like miracles, they were allowed to break the rules, so to speak. I am convinced that God enjoys messing up our neat systems so we will have to keep coming back to Him for truth. God's full truth will always be greater than any system man can conceive.