Dear Slavophile,
I was going to mention it . . .

Last year, as you will know, a ROC delegation brought relics of St Seraphim of Sarov together with an icon to the Abbot of Chevetogne.
The delegation was shown around the Byzantine monastery Church of St Benedict (with a wonderful icon of St Benedict in the iconostasis). Both Orthodox and Roman Catholic alike then knelt in veneration of the relics of St Seraphim.
The article by the Russian Orthodox written about the event was very irenical and complimentary. The article said that the Benedictines at Chevetogne have their "Byzantine-Slavonic section (or Orthodox)" (sic) not because they "seek to convert Orthodox, but to educate Western Christians about the Orthodox liturgical tradition."
The article went further and said, "The veneration of the relics of St Seraphim of Sarov brought by the delegation demonstrates the growing awareness and veneration of St Seraphim of Sarov in the Roman Catholic Church."
The monastery's online store sells excellent Orthodox crosses, icons and cd's of the hymns and services sung by their "Byzantine-Slavonic (or Orthodox)" choir!
Fr. Sergius Keleher (+memory eternal!) once said that if the Abbot feels that a certain monk does not have enough grounding in the Byzantine rite, he will give him longer assignments to the Byzantine Church at the monastery.
There are also the ruins of a Benedictine monastic foundation on Mount Athos as well. Jordanville Monastery has a translation of the Rule of St Benedict together with a Canon and Akathist to the Holy Father.
Alex