Update 10/14/2016: Hoping to post the primary source (bulls of Gregory XI in Aloysius Tautu) before 2017.
1. From Rev. Fr. Joseph M. Gill, S.J. of happy memory (1901-2006), Byzantium and the Papacy, 1198-1400 (Rutgers University Press, 1979), pp. 205-206:
Cantacuzenus told them that he had already, with the assent of the co-Emperor, subscribed a formal chrysobull giving the Pope his title and recognizing the primacy and universality of the Roman Church. He was ready to show the same obedience to the Pope as did the King of France and to unite the Empire with them, and that not just nominally but really.
The letter [of Pope Gregory XI] to Cantacuzenus was occasioned by a report of the Bishop John. He had told Gregory that, during a public debate held in the previous October between a group of Dominicans on their way to Armenia and Cantacuzenus with some other Greeks, Cantacuzenus had declared that "he believed and held that the holy Roman Church … possessed the primacy over all the Churches of the world and that he would willingly suffer death in defense of that truth, if it would help." The Pope urged him to use his erudition and influence to promote union and to protect Greek Catholics from molestation.903. Siméon Vailhé in "Constantinople, Église de" in Dictionnaire de Théologie Catholique (Paris 1907), 3.2:1399 (page 93 of 214 at hyperlink) says, "Néanmoins, il donnait lieu à de belles espérances, car cet exemple fut suivi de plusieurs autres et l'ex-empereur Jean Cantacuzène lui-même serait venu à Rome en habit de moine, pour abjurer ses erreurs et retourner ensuite a son convent." This means, "Nevertheless, [the personal submission of Emperor John V Palaeologus] gave rise to great hopes, because this example was followed by several others and the ex-Emperor John Cantacuzene himself would come to Rome dressed as a monk, to abjure his errors and then return to his convent." Unless I am misunderstanding the French, the sense is that John Cantacuzene did in fact come to Rome to renounce the schism. Emperor John V Palaeologus became Catholic in Rome in 1369, and concerning John V's relations with the popes, Vailhé, loc. cit., refers the reader to Augustin Theiner and Franc Miklošič, Monumenta spectantia ad unionem Ecclesiarum Graecae et Romanae (Vienna: Wilhelm Braumüller, 1872), 29-46. Vailhé does not give a date or a primary source for Joasaph's (John Cantacuzenus's) journey to Rome, but it must have been between 1377 (Pope Gregory XI's return to Rome) and the death of the ex-emperor in 1383 (during the reign of Pope Urban VI).
90 [Aloysius L.] Tautu, Gregory XI, nn. 136, 134, 135.
4. In the Synodikon of Orthodoxy the Eastern Orthodox Christians say, "To John Cantacuzenos, who is at rest with the pious, our ever-memorable, most pious and Christ-loving emperor, who by the divine and angelic Habit was renamed Ioasaph, Eternal Memory, Eternal Memory, Eternal Memory!"