Will ever the two meet? Unfortunately, I am pessimistic about any future reunion between the two. That is heartbreaking but it seems to me to be the real state of affairs. Any thoughts?
To get back to your original post, I shall answer the question posed form just my personal point of view.
Do I see a re-union of the two churches? No.
My thoughts on this a.k.a. why? Because God revealed the truth and showed us His complete plan once Jesus Christ established His Church and God placed His Spirit upon the Earth to guide Her. The Papacy of Rome decided that, through rationalist Western thought, certain issues must be brought up to better understand and explain, like communion and the Mysteries. After time, thing which are still outright unexplainable, but they happen, became doctrines and no longer Mysteries. Yet at the same time, new doctrines were made to try and explain the unexplainable Mysteries' explanations. Eventually this became so out of hand that doctrines were put upon doctrines to explain the explanations of yet more doctrines which the Section of the Catholic Church was starting to see some unexplainable things in the West as just a remnant of the Mystery itself.
After time, the Mysteries became doctrinal explanations and not so mysterious anymore. Funny names like Transubstantiation and Papal Primacy became common and to furthermore confuse Christ's Church the Pope himself started turning these created doctrines of explaning the unexplainable into the core principles of the Faith. Sadly this upset the whole Church and made everyone sad, except those who thought that these explanations of the explanations of the unexplainable Mysteries were a normal part of Jesus' Church.
So after some time of dealing with these unfortunate doctrinal issues and trying to show the Pope that the Mysteries are something that cannot be explained, the Pope began to believe that making up doctrines and using them as a rule of the CHurch, of course this is a rational humanistic approach to the unexplainable. He declared himself the Ruler of the Church, based solely on some of those explanations of the explanations of the unexplainable doctrines which turned Mysteries into "sacraments" and made Peter the "First Among Equals" into "Lord Ruler of Jesus Christ's Church, second only to Jesus Himself and Infallible" except of course the Magisterium yes-men. Needless to say, once the rest of the Whole Church said this was not right and Mysteries are unexplainable, the Pope of ROme took his notion elsewhere and started misbehaving, even enough to insult Christ's Mother, our Mother, and make her into something God never intended, a Co-Redeemer.
So this little explanation is why I do not see Rome ever playing fairly and not accepting the Truth of Her origins, simply because Rome tries to explain the unexplainable and eventually gets foot-in-mouth disease just about every century or two on some doctrine based on another doctrine trying to explain another doctrine which explains a doctrine which is just a mystery to everyone honestly, except God. So this is why I say "No".