Here are the draft translations that I commissioned of four letters. I don’t know whether any have been translated into English before. Now that I have paid for them, I can share them with you!
After reading the Turner article, it is clear that the letters are numbered 1-2000 in the manuscripts, and the Migne “books” are imaginary. So I’ve given the number in the collection as found in the mss, followed by the Migne book/letter reference. Anyone wanting to look at the Migne Greek can find it here.
35 (1.35) TO THE EMPEROR THEODOSIUS
If you are trying to gain the kingdom of Christ — may persistence unworn away crown this –, and the prize of immortality that God gives to those who administer it honestly, blend authority with mildness and lighten yourself of the weight of wealth by the necessary dispersion of it, for a king is not saved through ample power, nor does he escape the impiety of idolatry by keeping for himself abundant wealth.
310 (1.310) TO CYRIL OF ALEXANDRIA
Liking cannot see far ahead, while dislike cannot see clearly. So if you wish to remedy both of these sight problems, do not spout out such vehement statements, instead be more fair in your accusations. Even God All Knowing, before his birth, thought it best out of his love for man to come down and see the boisterousness  of the Sodomites, teaching us a lesson in fully inquiring. Many of the people who have come to Ephesus (are) ridiculing you for acting out of personal enmity and not for the doctrine of Jesus Christ. “Here’s this nephew of Theophilus, they say, imitating his way of thinking. Like him, he falls into a rage against the God-loving John, inspired by God, and he desires ever so much to lecture, even though there is a great difference between the people (who are) deciding.”
 There should be a better word for this.
1106 (3.306) TO THE BISHOP CYRIL.
Just as the emperor is subject to the laws, the law having a life of its own, so a priest is subject to the laws of the Lord, the canon being untouchable. 
 The Greek actually says the canon is “apthoggos” meaning that you can’t utter any words of protest against it.
1582 (5.268) TO THE BISHOP CYRIL.
Once the hierarchy used to correct and temper the office of emperor when it stumbled and fell, but now it has fallen beneath it, losing not its own rank, instead possessing ordained men unlike those in our ancestors’ time. Previously when those crowned with a holy office lived the evangelic and apostolic life, naturally the office of emperor stood in awe of the hierarchy, but now it is the hierarchy of the office of emperor. In my opinion, the office of emperor is following its natural course, since it has not intentionally meant to assault the hierarchy, which it reveres like a god, but avenge it of the assaults on it and temper the people not conducting themselves as they should toward it.
 Note the euphemism for the not so perfect bishops.
Comments and corrections are welcome!