Well, first of all, although I believe that I John 5:8 and II Corinthians 13:14 reflect Biblical theology, I don't use them in an academic discussion. Looking at the manuscript evidence, I don't think that Matthew 28:19 is a problem.
Secondly, these aren't the only Trinitarian statements. (Matt. 3:16-17, John 14:16-17 & 26, Gal. 4:6, Eph 2:18, II Thess. 3:5, I Peter 1:2, Eph. 1:3 & 13, Heb 9:14)
As for the formula, I am not a stickler for baptismal formula. It is the heart that matters, not the words. But if I have to choose, I believe that Jesus' direct instruction is sufficient as opposed to the various indirect statements of Acts.
The Trinity is the word that I use to describe my belief in these three Biblical truths.
1. That God is profoundly One.
2. That Jesus is God. That the Father is God. That the Holy Spirit is God.
3. That Jesus refers to and speaks to the Father as a separate person. That Jesus speaks of the Holy spirit as a separate person. That the writers of the New Testament spoke of the Father, the Son, and the Holy Spirit as distinct persons.
Either you must ignore one or more or these truths or belief some form of trinitarianism or believe that the Bible is at best inconsistant.
Okay...Matthew 3:16-17, Galatians 4:6, Ephesians 1:3&13, 2:18, Hebrews 9:14, and 1 Peter 1:2 hardly qualify as verses that could in any way make the case for the Holy Spirit as a person, much less a co-equal third person with the Father and the Son. Each of these verses mentions an activity or purpose of the Spirit which is by no means better understood if the Spirit were a full person rather than if the Spirit were simply understood as an extension of the Father's person and activity. In other words, there is no particular justification in these verses for describing the Spirit as a full person.
The remaining verses that you mentioned are John 14:16-17 & 26 (you also mentioned 2 Thessalonians 3:5, which doesnt mention the Spirit at all). In 14:17 Jesus says He will send the Spirit (future) who abides with them (present) and will be in them (future). The Spirit, then, is with and among the disciples, but not yet in them. Who does this describe perfectly? Jesus Himself.
Three Biblical truths:
1. God is profoundly One.
2. Jesus is "God with us". His body was the tabernacle (John 1:14) in which God dwelt. God (the One God, "all the fullness of the deity" Col 1:15) in-the-flesh, i.e. incarnate. He is the "Everlasting Father" or "Father of Eternity". The fully God-fully man Jesus is the Son of God because He is the One True God revealed in a new way (Heb 1:1-2)
3. That Jesus refers to and speaks of the Father as greater or more than just what the people were able to see when they looked at Jesus. Jesus was God incarnate, but God's presence was not limited to the flesh, even during His life. When you see Jesus you see the Father, but not as if you were beholding all that the Father is.
I affirm God the Father. I affirm that Jesus was God in the flesh. I believe that the Spirit is God continuing to dwell among and in us. I just don't believe that the Father is not Jesus or the Spirit, or that Jesus is not the Spirit. The One True God is the Father of all, and is also the One who revealed Himself in flesh and is also the One who continues to work in us as the Spirit.
My understanding is not unbiblical, not inconsistant; it is just different from yours. It is not LESS biblical nor LESS consistent than yours either. It comes from no source but the Bible, through and through.