I like the idea of "triunity" which is layman's terms for trinity, yes indeed. However, as you aptly show, each part IS God, so they aren't just a unity.
Perhaps it is easier to believe in the TRINITY (another word description of God, though not specifically used in Scripture) if we remember that God is Omnipresent. We have to expand our perspective (and maybe think in quantum physical/metaphysical terms) and realize that while it is God the Holy Spirit who indwells us, it isn't like God the Father is only in heaven, and God the Holy Spirit is only here... but that God in HIS expanse, is everywhere and not limited nor divided up into 3 parts as we humans have a tendency (imo) to think.
Good post, btw.
Another thought, we are not to pray TO the Holy Spirit, but to the Father, though the Holy Spirit is our mediator. We can ask anything of the Father because of the work of the Son on the cross.