“I’m not sure I see how this speaks to anything regarding the priest vs the bishop.”
The passage says nothing about a distinction between a priest and a bishop.I asked if it was the source of the Western notion that a priest is “Alter Christus”.
The position of the bishop, however, is indeed different from that of a simple priest. Some have argued that the theology of +Ignatius of Antioch leads to the conclusion that a bishop is an “Alter Christus”. I personally think that’s nonsense but it is more appealing and probably more soundly grounded than to say the same of the local parish priest.
I don't know if that is the origin, but somehow I think you might be misrepresenting Western Ecclesiology, as the priest is really the functionary of his bishop and must be in union with that bishop.
Dogmatic Constitution Lumen Gentium clearly states that priests are dependent on the bishops in the exercise of their power (LG 28).
And as far as the idea of "alter Christus, ipse Christus," consider this other quote from St. Augustine:
8. Let us rejoice, then, and give thanks that we are made not only Christians, but Christ. Do ye understand, brethren, and apprehend the grace of God upon us ? Marvel, be glad, we are made Christ. For if He is the head, we are the members : the whole man is He and we. This is what the Apostle Paul saith : " That we be no longer babes, tossed to and fro, and carried about with every wind of doctrine." But above he had said, " Until we all come together into the unity of faith, and to the knowledge of the Son of God, to the perfect man, to the measure of the age of the fulness of Christ." 3 The fulness of Christ, then, is head and members. Head and members, what is that ? Christ and the Church. We should indeed be arrogating this to ourselves proudly, if He did not Himself deign to promise it, who saith by the same apostle, "But ye are the body of Christ, and members."- Tract 21.8
Did not St John Chrysostom say,
For the priestly office is indeed discharged on earth, but it ranks among heavenly ordinances; and very naturally so: for neither man, nor angel, nor archangel, nor any other created power, but the Paraclete Himself, instituted this vocation, and persuaded men while still abiding in the flesh to represent the ministry of angels…For when you see the Lord sacrificed, and laid upon the altar, and the priest standing and praying over the victim, and all the worshippers empurpled with that precious blood, can you then think that you are still among men, and standing upon the earth? Are you not, on the contrary, straightway translated to Heaven, and casting out every carnal thought from the soul, do you not with disembodied spirit and pure reason contemplate the things which are in Heaven?
For if any one will consider how great a thing it is for one, being a man, and compassed with flesh and blood, to be enabled to draw nigh to that blessed and pure nature, he will then clearly see what great honor the grace of the Spirit has vouchsafed to priests…For it has not been said to them, Whatsoever you shall bind on earth shall be bound in Heaven, and whatsoever you shall loose on earth shall be loosed in Heaven. They who rule on earth have indeed authority to bind, but only the body: whereas this binding lays hold of the soul and penetrates the heavens; and what priests do here below God ratifies above, and the Master confirms the sentence of his servants…
…But our priests have received authority to deal, not with bodily leprosy, but spiritual uncleanness— not to pronounce it removed after examination, but actually and absolutely to take it away.
Tretise on the Priesthood III.4-6
I am not trying to say that St John stated or implied "alter Christus ipse Christus" in regards to priests, above. But he did indicate the tremendous dignity of the order and the incredible authority given that order by the Spirit.
The other thing I would suggest along those lines is the letter of Dionysius the Areopagite to the monk Demophilos. It is not really convenient to quote the whole letter, but in the context of this whole letter, I would ask you to read the vision of Carpus described in Section VI, paying particular attention to the words of the Lord Jesus to Carpus: Strike against Me in future, for I am ready, even again, to suffer for the salvation of men; and this is pleasing to Me, provided that other men do not commit sin… In the context of preceding content of that letter and the specifics about which he was rebuking Demophilos, it is fairly apparent to this Western mind the reason why Dionysius chose that particular tale. (See the quote from St Augustine above).
BTW, the Google Book extract you provided Maryz earlier unfortunately did not give the full text of the absolution in the rite described on p 59 (page 60 was not part of the preview). Fortunately, I was able to find it elsewhere:
May our Lord and God Jesus Christ, through the grace and bounties of His love towards mankind, forgive thee, my child, N., all they transgressions. And I, His unworthy priest, through the power given unto me by Him do forgive and absolve thee from all they sins, in the name of the Father and the Son and the Holy Spirit. Amen.
I assume the bolded text was the "Western influence" you were speaking of. (btw, here is a link to the Service book of the Holy Orthodox-Catholic Apostolic Church)