O... and this is interesting:
the Patriarchy of Moscow was founded in 1589. The last Partiarch of that line was Adrian, who served until 1700. He was replaced by a coadjutor, and then simply a head of the Russian Holy Synod.
The Patriarchy was re-established by the Communist Party, to create a centralized, state-run church.
I therefore even wonder if the Catholic Church should regard the Patriarchy as a representative of the Russian church at all. Naturally, if you are trying to restore the unity of the ancient Church, you like to have a partner in negotiations. If Alexy refuses to talk, however, maybe Benedict should talk with other Archbishops. I'd love to see Alexy's reaction to frutful negotiations with Belarussians or Estonians. OTOH, I can readily see how they'd be unwelcoming to a "back-door" talks.
Peter the Great did not allow a new Patriarch to be chosen after Patriarch Adrian's death, and it was he who created the Synod of Bishops.
In 1917 the Synod of Bishops elected a new Patriarch of Moscow and All Russia. This was was Patriarch Tikhon.
Patriarch Tikhon was not affiliated with the Communist party except that he lived under their rule. He resisted them in every way possible and was arrested for this.