Thank you, dear brother in Christ, for your beautiful meditation!
That you thought it through in terms of "relative dimensionality" is particularly intriguing to me.
You point out that the best man can achieve is to come "very nearly to His limits, but not quite." This coheres very well with my own understanding of man as imago Dei, the creature made in the image or "reflection" of God. God is Source: we are reflections. Ineluctably, there is a categorical difference here of cosmic proportion.
And that categorical difference suggests that man can never be god himself — there is an insurmountable chasm between the divine and its human image.
I do believe that Jesus Christ incarnated as a man and suffered most grievously to die for us on the Holy Cross, so to pay the blood price for the sins of men, imputed to them since Adam's Fall, that they may be redeemed. And on the third day, He rose again from the dead, and was resurrected unto His Father in heaven. Thus our Lord Jesus Christ shows us, in the entire Crucifixion drama, the future of every living soul who loves Him in faith, hope, and love of neighbor.
God alone knows how many dimensions there are. But it seems to me for the above reasons that man vis-a-vis God will always come up at least one dimension short. For the image is not the Source.
Your wrote:
"...when we see Him, we shall be like Him."Yes!!! But the operative word here is "like Him"; which does not mean "same as He."
I just mention this to dissuade people who might think there's any kind of beneficent pay-off in actual reality for exercises in "self-divinization." Examples: Hegel's Phaenomonologie; Nietzsche's Ubermensch; Obama's presidency....
If you were to ask me, these all signify Second Realities. All sound and fury, signifying nothing.... Going nowhere, and causing as much misery as possible along the way to Nowhere. Thomas More coined a term for this "Nowhere": he called it Utopia.
I'd better put a sock in it for now, dear brother!
Thank you so very much for writing, dear MHGinTN!