So with the functional ending of the EOx-OOx schism (as evidenced by the canonical transfer in Britain of an EOx priest to the OOx, from the Greek Orthodox Church of Antioch to a church that's part of the Coptic Church) it seems the OOx have modified their claim to include the EOx. Is that right?
The matter of the transfer of a priest is only one small aspect. The Patriarchates of Alexandria have synodically produced a document that states that families with members in both communities may receive all of the sacraments in either community. This is a restricted but complete inter-communion.
The Antiocheans and Syrians in the Middle East have produced a document that allows for the reception of all the sacraments from either church to deal with the situation in many rural areas where there are few enough Syrians of either community. This is again a restricted but complete inter-communion.
I know EO's who commune in OO churches through isolation and need, not religious tourism, and I know OO's who commune in EO churches for the same reasons, and I know that bishops condone and support such grass-roots inter-communion.
The OO have said in Synods in many churches for many years now:
"In the light of our Agreed Statement on Christology as well as of the above common affirmations, we have now clearly understood that both families have always loyally maintained the same authentic Orthodox Christological faith, and the unbroken continuity of the apostolic tradition, though they have used Christological terms in different ways. It is this common faith and continuous loyalty to the Apostolic Tradition that should be the basis for our unity and communion. "
If we have a common faith, if the substance is identical, then it is sin not to do everything possible to be reconciled. The theology isn't that complicated. I think that we will have a lot to answer for if we do not make every effort 'to be one'.
What the OO are saying is not a variant of the 'branch theory' but that we have determined that the EO are qualitatively Orthodox in faith. They are the Orthodox Church even as we have always been the Orthodox Church. We may be separated but we have both, through grace, been able to preserve the Orthodox faith. I am not sure that this view encompasses the Roman Catholic church in the same way. In that case I believe there is a greater sense of economia. The modern Ronan Catholic church is not the same as the West Roman Church that the OO walled themselves off from, to preserve their Orthodox faith, 1450 years ago.