The problem with your argument is you cannot define the biblical God is anything but Trinity.
To do so constitutes another god.
The apostle John I thought was able to define who we need to believe in quite adequately. I think if we followed his lead, we can't go wrong.
KJV 1 John 1
3 That which we have seen and heard declare we unto you, that ye also may have fellowship with us: and truly our fellowship is with the Father, and with his Son Jesus Christ.
KJV 1 John 2
22 Who is a liar but he that denieth that Jesus is the Christ? He is antichrist, that denieth the Father and the Son.
23 Whosoever denieth the Son, the same hath not the Father: (but) he that acknowledgeth the Son hath the Father also.
24 Let that therefore abide in you, which ye have heard from the beginning. If that which ye have heard from the beginning shall remain in you, ye also shall continue in the Son, and in the Father.
25 And this is the promise that he hath promised us, even eternal life.
KJV 1 John 3
23 And this is his commandment, That we should believe on the name of his Son Jesus Christ, and love one another, as he gave us commandment.
24 And he that keepeth his commandments dwelleth in him, and he in him. And hereby we know that he abideth in us, by the Spirit which he hath given us.
KJV 1 John 4
12 No man hath seen God at any time. If we love one another, God dwelleth in us, and his love is perfected in us.
13 Hereby know we that we dwell in him, and he in us, because he hath given us of his Spirit.
14 And we have seen and do testify that the Father sent the Son to be the Saviour of the world.
15 Whosoever shall confess that Jesus is the Son of God, God dwelleth in him, and he in God.
16 And we have known and believed the love that God hath to us. God is love; and he that dwelleth in love dwelleth in God, and God in him.
KJV 1 John 5
16 If any man see his brother sin a sin which is not unto death, he shall ask, and he shall give him life for them that sin not unto death. There is a sin unto death: I do not say that he shall pray for it.
12 He that hath the Son hath life; and he that hath not the Son of God hath not life.
13 These things have I written unto you that believe on the name of the Son of God; that ye may know that ye have eternal life, and that ye may believe on the name of the Son of God.
I see nothing in the above that says we should believe in some formula devised by the church to describe or define the Godhead.