Except every Orthodox Church I know of does recognize a primacy of Rome
Not necessarily. Some do not recognize primacy of current Rome… they recognize that Rome has claim to primacy but since they claim supremacy, they forfeit primacy too. You can’t have primacy in Orthodox Church unless you are actually member of it…
From my reading and understanding of these documents, I would say that Rome sees that the “schism” between we Orthodox and you Catholics is from within the Church and that our lack of communion with each other is more of an upper management issue.
Unitatis Redintegratio must be read within light of tradition, as entire Vatican II. Since Ut Unum Sint references Vatican II and Unitatis Redintegratio, it has to be understood same way, by transitional logic. I do not quite think that upper management does not matter, and neither does Rome. If that were indeed the case, Rome would not need to defend it’s primacy nor infallibility, nor status of being True Church, and could just convert to Orthodoxy for the sake of it. I am not sure where does Balamand Statement imply this to be honest. It goes against Catholic teaching.
Orthodox Church possesses true sacraments and true faith, but they lack unity with Church. Something that can be said about sedevacantists or any schismatics from any Catholic or Orthodox Church (Old Calendarists being prime example there). This method would justify schism of any Bishopric, and is not in accordance with what we believe.
It is Canon Law that a Latin Rite Catholic cannot replace the Catholic mass with an Orthodox mass.
Catholic of any rite should not substitute Catholic Liturgy for Orthodox/Sedevacantist/Any other Liturgy, however valid.
Quoting wikipedia about Canon 844:
" Considering that Norm 132 “specifies Church in the universal sense, and not Church
sui iuris ,” Vere points out that, “this norm cannot be interpreted in the sense that the Catholic is unable to approach a Catholic priest of his own liturgical rite.”"
So according to canon lawyer, even if Latin Catholic was simply stuck in a land where only Byzantine Catholics and Sedevacantists operate, he would be obliged to attend Byzantine Catholic Divine Liturgy and not Sedevacantist Mass. Same way, Byzantine Catholics in strictly Latin Catholic country should attend Latin Catholic Mass on higher priority than Orthodox Divine Liturgy. Unity of the Church precedes Rites.