Does the Church of Christ "subsist" in the Orthodox Churches?

You all know that the Second Vatican Council declared:

The sole Church of Christ [is that] which our Saviour, after his Resurrection, entrusted to Peter's pastoral care, commissioning him and the other apostles to extend and rule it.... This Church, constituted and organized as a society in the present world, subsists in (subsistit in) the Catholic Church, which is governed by the successor of Peter and by the bishops in communion with him [LG 8# 2].

You will also be familiar with the fact that the phrase "subsistit in" was chosen in favour of the simpler affirmation "The Catholic Church IS the Church of Christ". As is also well known, the Council Fathers wished to affirm that:

some and even very many of the significant elements and endowments which together go to build up and give life to the Church itself, can exist outside the visible boundaries of the Catholic Church: the written word of God; the life of grace; faith, hope and charity, with the other interior gifts of the Holy Spirit, and visible elements too. All of these, which come from Christ and lead back to Christ, belong by right to the one Church of Christ. (UR 3)

But close observers will note that the Catholic Church has never taught that the true Church of Christ "subsists" in any sense at all in the local Churches and ecclesial communities not in communion with the See of Peter. This is a point highlighted in an essay by Fr Adriano Garuti OFM called "Sister Churches: Reality and Questions" (published as an appendix in The Primacy of the Bishop of Rome and the Ecumenical Dialogue, Ignatius Press 2004). He discusses a point made in the CDF document Communio Notio which says:

Since, however, communion with the universal Church, represented by Peter's Successor, is not an external complement to the particular Church, but one of its internal constituents, the situation of those venerable Christian communities also means that their existence as particular Churches is wounded.

, and makes the following conclusions:

In fact, full incorporation into the Church, which confers the fullness of ecclesial status, is not realized simply by "the bonds of the profession of faith and of the sacraments", but also through the bodns of "ecclesial goverenment and communion", which is to say that it presupposes the acceptance fo the "integral structure" of the Church. The one and only Church of Christ, therefore, "subsists in the Catholic Church, which is governed by the Successor of Peter and by the bishops in communion with him"....

The Orthodox Churches, in contrast, inasmuch as they possess certain elements of sanctification and of truth--especially apostolic succession and valid Eucharist--do have meaning an d importance in the mystery of salvation and are instruments at the service of the Spirit of Christ, and hence they too participate in the proper mission of the Church of Christ, with which they have a partial relationship.

Then comes the shot that strikes right between the eyes:

In any case, the said elements "cannot be the subject of the 'subsistence' of the Church itself, because if this were the case, the one and only Church of Christ would be a plurality of Churches, in each of which it subsists in equal measure."

We Catholics are used to hearing the Orthodox Churches claim that we are not a true Church, because the only True Churches of Christ are the Orthodox Churches. As Garuti quotes one Assimakis: "Greek theology today firmly maintains that the non-Orthodox do not belong to the Church any more." There was a time when Catholics also denied any ecclesial reality at all beyond the visible boundaries of the Catholic Church. But the position outlined here is surely much starker than many post-Vatican II ecumenical type Catholics (such as your humble blogger) have been wont to think. Garuti concludes:

that although the Orthodox Churches possess elements of ecclesial status, the Church of Christ does not subsist in them: they are Churches, but in an imperfect and analogous manner with respect to the Church, from which they derive their existence and salvific efficacy.

I understand his point, and accept it in the main, but remain a little uneasy about the idea that the true Church of Christ does not in any sense "subsist in" the particular local Orthodox Churches--in at least some diminished (or, to use the CDF term "wounded") manner--if only because they have retained the valid Eucharist. This approach seems to make the Eucharist only an "element" of the True Church, rather than "source and summit" of the Church itself. The Second Vatican Council and the CDF have both affirmed that the Church of Christ subsists fully in the Catholic Church, but have steered clear of affirming whether it does or does not subsist in any way beyond the visible boundaries of the Catholic Church.