Here is my proof for not baptizing in the name of the Father, Son and Holy Ghost:
Isaiah 2: 2-3, The word of the Lord that goeth forth from Jerusalem will build the house of the God of Jacob. I do not find Galilee as the city chosen of God for the building of His church.
John 13:20, He that receiveth whomsoever I send receiveth me, and he that receiveth me receiveth Him that sent me. This points us to the apostles.
The Comforter, which is the Holy Ghost, will teach you all things, guide you into all truth, and bring to your remembrance all things whatsoever I have said unto you, John 14:26 and John 16:13. Jerusalem
I pray not for these alone, but for them also which shall believe on me, “Through their word” John 17:20, which also points to the apostles word.
There is no authority for baptizing in the name of the Father, Son, and Holy Ghost. Yes, Jesus spoke these very words to eleven disciples, but not twelve. Their number was incomplete at Galilee.
Here is a classic case of artifical restriction. You acknowledge that Jesus' words in Matthew 28:19-20 defeat the point that baptism should be done in the name of Jesus only, so you have sought a way to claim that Jesus' words at this moment in time are not binding on Christians. The essence of your argument is that the teaching did not take place in Jerusalem and that it was given only to eleven disciples since Judas Iscariot had committed suicide.
By such reasoning, one would have to discard 90% of the Gospels because Jesus taught in many regions of Israel. There are only a few instances of teachings that actually take place in Jerusalem. The flaw is that the apostles cite Jesus' teachings as proof, regardless of where Jesus made the statement. As an example, Paul cites Jesus' teaching on divorce and remarriage in I Corinthians 7:10-11, which Jesus made in the region beyond the Jordan (Matthew 19:1,9) and on a mountain in Galilee (Matthew 4:23; 5:32).
A second flaw in this reasoning is that you claim that the writings of the apostles are binding, but you ignore the fact that Matthew 28:19-20 was recorded for us by the apostle Matthew who wrote the book after the founding of the church. If the apostle's writings have weight, then Matthew 28:19-20 cannot be ignored.
Third, the Hebrew writer points out: "For a testament is in force after men are dead, since it has no power at all while the testator lives" (Hebrews 9:17). A testament (or will or covenant) must first be given, then the testator dies, then the testament comes into force. The words that Jesus spoke were his testament for the coming age. He then died, and his words went into effect. "And you, being dead in your trespasses and the uncircumcision of your flesh, He has made alive together with Him, having forgiven you all trespasses, having wiped out the handwriting of requirements that was against us, which was contrary to us. And He has taken it out of the way, having nailed it to the cross" (Colossians 2:13-14). The words that Jesus spoke to the apostles after his death and before his ascension are still the words of the Son of God. Notice what he said, "All authority has been given to Me in heaven and on earth. Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all things that I have commanded you; and lo, I am with you always, even to the end of the age" (Matthew 28:18-20).
Jesus spoke based on the fact that He holds all authority both in heaven and on earth. Upon that authority he charged the apostles make disciples from all the nations. The means of fulfilling that commission was through baptism in the name of the Father, Son, and Holy Spirit. Further, they were to teach these disciples to do all the things Jesus had command these apostles, which would include this current command to make disciples of all the nations. Finally, the duration of the command is stated when Jesus said that He would be with them to the end of the age. This command has no repeal.
Did it make any difference that at the time of this statement to the apsotles that Jesus only had eleven living apostles? Obviously, it didn't make a difference to Jesus since he gave them the charge that would be binding to the end of the age. By stating that the teachings would only be effective when there were twelve apostles would make the teachings of Peter and John of no effect since their writings (especially John's) took place after many of the apostles had already died. In a useless attempt to invalidate a clear teaching of Jesus, you placed emphasis on the number of apostles instead of the duty of the apostles to teach and record the words of Jesus. The authority for the apostles writings come not from the apostles, but from the one who commissioned them -- Jesus, the Son of God. What they wrote were not their own words, but what Jesus wanted them to write as they were guided by the Holy Spirit. "Now we have received, not the spirit of the world, but the Spirit who is from God, that we might know the things that have been freely given to us by God. These things we also speak, not in words which man's wisdom teaches but which the Holy Spirit teaches, comparing spiritual things with spiritual" (I Corinthians 2:12-13). The words of Jesus that Matthew recorded for us have all the authority of the Lord Jesus Christ behind them.