I don't know any Trinitarians at all who think that there are three Gods in one God. I do know a lot of Trinitarians who believe that there are three Persons who make up the one God. But then, it's much easier to debunk a doctrine if you first distort what it teaches, isn't it?
That would be me. As much as I've read those words in Trinitarian literature, I have to admit they don't quite sink in like they have with you. I'm probably guilty of distorting the Trinity doctrine if it really teaches that the three Persons make up one God, but that each person is only a personality of God. I always got the impression that true believers in the Trinity actually do teach exactly that (3 Persons = 1 God, not 3 Gods = 1 God) but that this formula is more of a "posture," used only in the circumstance created when the required language becomes too obviously polytheistic. At all other times, when no one is questioning the doctrine, Jesus = fully God, the Father = fully God, and Holy Spirit = fully God. In fact, just as in NT practice, the Father becomes the primary person equated with God, which puts Trinitarians at even less variance with the unspoken beliefs of Jehovah's Witnesses.
If the Father is fully God and Jesus is fully God, and they are both true, then we have two true Gods. If the Father is God and the Word is God then we have two Gods. If the Son/Messiah is Mighty God and the Father is Almighty God then we have two Gods.
If three persons are fully King, even if they meet and work together, see each other, represent each other and are sent by/from each other, we still have three Kings.
Rom 15:6: so that...you may glorify the God and Father of our Lord Jesus Christ.
1 Cor 8:6: yet for us there is but one God, the Father, from whom all things came and for whom we live; and there is but one Lord, Jesus Christ, through whom all things came and through whom we live.
Eph 4:6 4 There is one body and one Spirit--just as you were called to one hope when you were called-- 5 one Lord, one faith, one baptism; 6 one God and Father of all, who is over all and through all and in all.
1 Thess 3:13 May he strengthen your hearts so that you will be blameless and holy in the presence of our God and Father when our Lord Jesus comes with all his holy ones.
I know this subject gets beaten to death, but it's my first time discussing it. I should let you know that I do believe that the Gospel of John teaches exactly what you say (2 Persons = 1 God) and until just a few minutes ago, I used to think that John taught it very subtly so that it would sink in rather than offend the sensibilities of fellow Jewish/Christian monotheists. but I now believe that, although the language was necessarily careful, it is a lot more precise than I used to think. I have just reread a lot of John after your post above and I realize that John seems even more clearly in line with the definition you gave. It was JW baggage I've carried for 20 years that kept me from seeing it as simply as you put it.
Yet, although I could accept that John promoted that doctrine or definition consistently, I see nearly the opposite belief expressed consistently in nearly all (about 100) other "proof texts" with maybe 4 exceptions. Problem is, even those exceptions are ambiguous to me. If the Trinity was a necessary and "true" doctrine in the first century, it seems that John is the only writer who gets it (or, for whom the Spirit has revealed all things).
Gamaliel