I may be incorrect about this, but I think St. John the Merciful (St. John Eleimon) is also venerated by the Coptic and Ethiopian Churches. He was the Chacedonian Patriarch of Alexandria in the early seventh century, and was renowned for his meekness and almsgiving. He showed great tolerance and kindness to the Non-Chalcedonians in contrast to the violence that had been practiced against them, and strove towards reconciliation between the Churches. If indeed the Coptic and Ethiopian Churches recognise him, I would have to say that he would be a great hope for us all.
I couldn't find any mention of him in the Synaxarium, though His Holiness Pope Shenouda III does refer to a "St. John the Merciful" in a few of his writings. Although H.H. mentions nothing of his ecclesiastical position, he does depict him as one who was renowned for his charity to the poor; this suggests that he could very well be referring to the Chalcedonian Patriarch you have in mind given the fact that that very Patriarch seems to be alternatively known as St. John the Almsgiver.
I believe there are a few more Chalcedonian Saints who are recognised as such according to various OO traditions. Empress Theodora, the wife of Emperor Justinian, for example, is recognised as a Saint by virtue of the fact she offered protection to many OO Bishops who were threatened with persecution under Emperor Justinian's reign and she offered refuge to OO heirarchs who were forced into exile, in her very own palace.
On the other hand, there are Non-Chalcedonian figures who are recognised as Saints according to various EO traditions. The EO Church of Georgia, for example, venerates St. Peter the Iberian, St. David of Garesga, and St Eustace of Metskheta.
Then again, there are non-Ephesian and non-Chalcedonian figures (i.e. Nestorian) who are recognised as Saints by both our Churches e.g. St. Isaac the Syrian.