Interesting thoughts.
I tend to think that being "created in the image of God" has to do with the fact that we are the only beings He created which share His triune nature. Like God, we have a body (Son), mind/soul (Father) and a Spirit. Angels and demons have souls and spirits; other animals have bodies and spirits, but we are the only critters that have all three.
Woe! Where do you make up this nonsense? I'm just writing a paper on 'the image of God" which only appears in Scripture 5 times, but is a very important concept, about both who God is and who we are in relationship to him.
First, let's look at what the Trinity really is. The Trinity is the definition of who God is. First, God is one! He is one God or ousia (Gk) or being. He is triune, because he consists of three persons, persona in Latin, or hypostasis in Greek. God is not modal, meaning the body is in Jesus, the mind is the Father and the Spirit is ?? You never posted that. The Father, Son and Spirit are the same in essence, with different functions. The Father, is not the mind of the Trinity. Both the Son and the Spirit have their own minds, being a part of their person or hypostasis. A disembodied Spirit is not God, nor is a body! Instead, all three have the Oneness of God, starting in the OT, with the Shema in Deut 6:4, "Hear, O Israel: The Lord our God, the Lord is one." God is one God, but as the early Christians knew, this same God revealed himself in the person of Jesus, the head of the church and Lord of all creation. (John 1:1; 20:28; Romans 9:5; Titus 2:13)
Yet, Jesus is clearly differentiated from the Father, thus revealing the Father as the first person of the Trinity and Jesus as the second person of the Trinity. The Father and Son are equal, the Father is not the mind of Jesus, although they perfectly agree on everything. Finally the Spirit has been amongst God's people, leading and guiding them, since the Day of Pentecost.The Spirit is not an "it" (regardless of the neuter gender of the Greek pneuma!). The Spirit is spoken of in personal terms. The writers of the NT use masculine terms, to make him a person, rather than a thing. The attribute to the to the Spirit aspects of personality, such as intellect, will and emotion. (1 Cor. 2:10; 12:11; Romans 8:26-27) The Spirt is noted as being God in Acts 5:3,4, in that by Ananias and Sapphire lying to the Holy Spirit, they had lied to God.
I object most to your characterization of the Trinity in a structural view, which seems to consist of three chopped up parts of God, that we in some way reflect?? In fact, the Trinity is relational. The personhood of the Father, Son and Holy Spirit is relational. To be created in the image of God is not to mimic in some way the form of the Trinity, but rather their relationship in the immanent Trinity, and to us in the economic Trinity.
The imago dei views the divinely given human calling to be the image of God, as a social reality. Eschatologically speaking, the relational life of the God who is triune comes to representation in the communal fellowship of the participants, which is the church, and the community of God.
Finally, the theological assertion that "God is love" (1 John 4:8,16) indicates the bonding that characterizes the divine life stands as the transcendent archetype for the dialectic of differentiation and commonality present in the Trinity. The eternal generation of the Son constitutes the first trinitarian person as the Father of the Son, and the second person as the Son of the Father, yet the two are bound together by the love they share, a bond that characterizes the divine nature as a whole, but also emerges as a separate hypostasis in the third person, the Holy Spirit. This shared love is the Holy Spirit, who nevertheless is not the Son, nor the Father and therefore differs from both.
The doctrine of the Trinity teaches that the trinitarian persons share in the divine essence, for there is but one God; yet they differ form one another, for each is a distinct person who; cannot be equated with, or subsumed within the others.
As far as the divine image, we are not merely some toy put together with three parts so we imitate God. Instead, the imago dei is a deeply relational concept, in which God created us to have a relation and fellowship with him, which was marred in the Fall.
So, just for curiosity's sake, where did you come up with your erroneous and limited definition of the Trinity, and the image of God? Did you make it up yourself? I just wonder, because I have never heard it put in such an odd way, and I thought I was familiar with all the various trinitarian heresies.