I'm currently at university myself, with the Middle Ages as my area of expertise. It seems the emperor in Constantinople was only amenable to the idea when he needed to persuade the Pope to help him. Thus, was there ever a genuine instance where the churches were extremely close to finding common ground, or was it all talk and wishful thinking?
Actually they were united once again on the Council of Florence in 1439. Byzantine emperor John VII agreed to this union in hopes of engaging western European countries in their struggles against Turks, although the majority of Byzantine church officials and people were against it, including Marcus of Ephesus, one of the most influential Byzantine bishops, who refused to sign the treaty. However the union didn't have any major significance, especially after Constantinopole fell to Turks.