On the first site, there is a citation from “Conversations with Patriarch Bartholomew” by Olivier Clement, regarding the eastern spirit of oecumenae “Moving beyond polemics, we need to reflect on a period of ecclesial life in which tensions were resolved not against the pope or against the councils, but in a different way”.
I looked through few pages of the site but, unfortunately, failed to find references to church leader's or council's blessing to this orthodox female monastic initiative in the West.