Rather than proof texting the Fathers or referring to a local, unusual Synod, which you fail to even exegete, you might just ask (humbly) the Orthodox posters here if they believe in the Latin view of purgatory. Cavaradossi explains well the Orthodox distinctions. Or better yet, ask an Orthodox priest.
The quotes were provided for someone else. Secondly They speak for themselves and don't need a rocket scientist or super theologian to understands the words written. They are very straight forward.
The quotes may have been provided for someone else, but if you only wanted him to respond to them, you should've sent them to him privately. If you're going to post them here, however, don't be surprised if others respond as well.
Actually, these quotes are not as straightforward as you want to make them out to be. I don't have the time to search out their context, but as you've presented them, most of them agree with the Orthodox position, and could be made to agree with the Latin position if you read that into the quotes and assume that "both are saying the same thing". But since the Latin teaching on "Purgatory" involves a bit more than just a post-death pre-resurrection cleansing, you really do have to read it into the texts or stretch the meanings of terms to make it fit.
I apologize, I nearly forgot about this. Forgive me
Clement of Alexandria
The believer through discipline divests himself of his passions and passes to the mansion which is better than the former one, passes to the greatest torment, taking with him the characteristic of repentance for the faults he may have committed after baptism. He is tortured then still more, not yet attaining what he sees others have acquired. The greatest torments are assigned to the believer, for God's righteousness is good, and His goodness righteous, and though these punishments cease in the course of the expiation and purification of each one, "yet" etc. (Patres Groeci. IX, col. 332 [A.D. 150-215]).
Are we even sure that this is talking about what happens to the soul after death? ISTM it could also be some sort of allegory on ascetic struggle (it says "the believer through discipline
", not "through death"). Even if it is talking about death, I don't think we can understand this without context. What does discipline have to do with it? What mansion is better than the former mansion which also includes the "greatest torment"? Who/what is doing the torturing? And what is the rest of the sentence that gets cut off by "etc."?
If a man departs this life with lighter faults, he is condemned to fire which burns away the lighter materials, and prepares the soul for the kingdom of God, where nothing defiled may enter. For if on the foundation of Christ you have built not only gold and silver and precious stones (I Cor., 3); but also wood and hay and stubble, what do you expect when the soul shall be separated from the body? Would you enter into heaven with your wood and hay and stubble and thus defile the kingdom of God; or on account of these hindrances would you remain without and receive no reward for your gold and silver and precious stones? Neither is this just. It remains then that you be committed to the fire which will burn the light materials; for our God to those who can comprehend heavenly things is called a cleansing fire. But this fire consumes not the creature, but what the creature has himself built, wood, and hay and stubble. It is manifest that the fire destroys the wood of our transgressions and then returns to us the reward of our great works. (Patres Groeci. XIII, col. 445, 448 [A.D. 185-232]).
This need not be the Latin "Purgatory". If the "fire" talked about is just a metaphor for a cleansing, the mechanism of which we don't really understand, then fine--that would be an acceptable way of trying to explain it. But there's a reason why Latin apologists look specifically for "fire" references and not merely for "cleansing". And it seems from my reading of this quote that the "fire" is being used metaphorically, unless we are also to take literally that the soul after death takes with him wood and hay and stubble that needs to be dumped before entering heaven or that God is literally a fire.
It is one thing to stand for pardon, another thing to attain to glory; it is one thing, when cast into prison, not to go out thence until one has paid the uttermost farthing; another thing at once to receive the wages of faith and courage. It is one thing, tortured by long suffering for sins, to be cleansed and long purged by fire; another to have purged all sins by suffering. It is one thing, in fine, to be in suspense till the sentence of God at the Day of Judgment; another to be at once crowned by the Lord (Letters 51:20 [A.D. 253]).
Again, what's the context? Without knowing that, it's impossible to say it definitely means what you think it means.
Ambrose of Milan
Give perfect rest to thy servant Theodosius, that rest which thou hast prepared for thy saints… I have loved him, and therefore will I follow him into the land of the living; nor will I leave him until by tears and prayers I shall lead him wither his merits summon him, unto the holy mountain of the Lord (Funeral Sermon of Theodosius 36-37 [A.D. 395]).
What about this suggests Latin "Purgatory" as opposed to the value of prayer for the departed in a general sense?
There is an ecclesiastical discipline, as the faithful know, when the names of the martyrs are read aloud in that place at the altar of God, where prayer is not offered for them. Prayer, however, is offered for other dead who are remembered. It is wrong to pray for a martyr, to whose prayers we ought ourselves be commended (Sermons 159:1 [A.D. 411]).
First of all, as above, this doesn't seem to argue "Purgatory" as much as it does "prayer for the departed". That said, it's just not correct that we don't pray for the martyrs. We certainly pray "to" them, but we also pray "for" them and "with" them. That much is clear from our liturgical texts and rites. Perhaps in the Western tradition you make or have come to make Augustine's distinction, but it is certainly not universal.
Temporal punishments are suffered by some in this life only, by some after death, by some both here and hereafter, but all of them before that last and strictest judgment. But not all who suffer temporal punishments after death will come to eternal punishments, which are to follow after that judgment (The City of God 21:13 [A.D. 419]).
So far, this is the first quote you've presented that, to me, argues for the Latin view.
That there should be some fire even after this life is not incredible, and it can be inquired into and either be discovered or left hidden whether some of the faithful may be saved, some more slowly and some more quickly in the greater or lesser degree in which they loved the good things that perish, through a certain purgatorial fire (Handbook on Faith, Hope, and Charity l8:69 [A.D. 421]).
Is this arguing that Latin "Purgatory" definitely exists, or that it is an acceptable and reasonable proposition explaining post-death purification? It's "not incredible", "can be inquired into and either be discovered or left hidden
", etc. I can see the appeal, but it need not mean what you want it to mean.
That allegory of the Lord [Matt. 5:25-26] . . . is extremely clear and simple in its meaning . . . [beware lest as] a transgressor of your agreement, before God the judge . . . and lest this judge deliver you over to the angel who is to execute the sentence, and he commit you to the prison of hell, out of which there will be no dismissal until the smallest even of your delinquencies be paid off in the period before the resurrection. What can be a more fitting sense than this? What a truer interpretation? (The Soul 35 [A.D. 210]).
You want this to mean Latin "Purgatory", and it could mean that. But besides wanting to know the context or what's missing where all the . . . 's are, I'm curious about what I bolded above. What does it mean that people can be confined to hell "until the smallest even of your delinquencies be paid off"? Is Tertullian teaching something along the lines of universal salvation? It wouldn't make sense to be there until you pay your debts, but then stay there forever because there's no escaping hell, right? Or is it common for Latins to refer to "Purgatory" as "hell"? In my experience, it is never the case, but maybe you'll surprise me.
Anyway, out of everything you provided, the quotes which most supported your position are from early Church fathers who either went wrong themselves or whose writings were used to support wrong notions as if they held them. Everything else is less straightforward than you think. It could mean what you want it to mean, but that post alone doesn't demonstrate it.