Thank you Mungo, that was an excellent explanation, in that it was, first of all, comprehensive, and secondly, that you sincerely and astutely addressed the shortcomings. You didn't claim to comprehend the incomprehensible.
Just so you know (maybe you do already), I am anti-trinitarian. But, my following contentions are at a fundamental level, so, I believe, that they should be valid irrespective of one's convictions on this matter.
We are created in God's image, there exists, therefore, an affinity between humans and God - 'be ye holy, as I am holy'. That is, we understand God's character and attributes as far as the definitions of those attributes are concerned. What we cannot fathom or comprehend is the magnitude of each of those characteristics. Existence we understand, omnipresence we do not. Knowledge we fully understand, omniscience we do not. Love and righteousness we are able to emulate, but perfection in these traits often elude us, ...but are not beyond our reach as the previous statement implies, and as the Mosaic Law stipulates. God is a personal deity who interacts and communicates with us on an individual level, we are individual persons with one consciousness, respectively.
But, when one tries to explain God with contradictions and implausibilities, this is where we conclude that one's exegesis is incorrect.
Having three all-powerful persons in one being or entity is a profound redundancy, when only one is required to create the universe, answer all the prayers of men, intervene in human events, provide all maintenance and providence of the universe, etc...
A god-man is an oxymoron in that all that defines divinity, is antithetical to that which defines humanity. God is immortal, man is mortal. God is transcendent, man is secular. God is immutable and incorruptible, man is corporeal and susceptible to decay. God is omnipresent, whereas man is circumscribed in space and time. God is infinite, man is finite, etc...
Thus, I don't believe that trinitarian theology has accurately understood or expressed, what God had intended to convey in His Word. That it, it is your initial predicates that are incorrect, and therefore you are attempting to put a square peg in a circular hole, and will invariably be obligated to capitulate at some point in your thesis on how to achieve this.
Namely: 'For example consider Jesus Christ. We believe he has two natures, human and divine, yet he is one person, the second person of the Trinity.' and 'The whole divine economy is the common work of the three divine persons. For as the Trinity has only one and the same natures so too does it have only one and the same operation: '