If "the Vatican is open to a less intrusive role for the pope in the Eastern churches than in the West", then Rome could start immediately with actual actions by removing the yoke it imposed on the Eastern Catholic Churches.  As it is, Patriarchs, heads of Churches with the same rank as the pope, minus the Petrine ministry, answer to a cardinal.

As a matter of fact, which Orthodox Church would like to find themselves in the same position? If anything, the status of the Eastern Churches under Rome is the surest fact on the ground that keeps the Orthodox away.