You keep bringing up the exedra as a point of reference, when it was a later addition to the aqueduct, and one of the authors you sourced favoured an earlier date, 147-151 range, for its construction. Yet you suggested a date that was not even noted by the author as a possibility.
Peregrinus didn't rail against the aqueduct for sixteen (4 Olympias) years. Instead, he railed against it and Herodes at one Olympia, not long after it had opened; but by the following Olympia four years later, he had rescinded his criticisms and announced his intentions to burn himself alive.
Peregrinus cannot be the same Polycarp that Irenaeus referred to in his
Letter to Florinus. Observe:
These opinions, Florinus, that I may speak in mild terms, are not of sound doctrine; these opinions are not consonant to the Church, and involve their votaries in the utmost impiety; these opinions, even the heretics beyond the Church's pale have never ventured to broach; these opinions, those presbyters who preceded us, and who were conversant with the apostles, did not hand down to you. For, while I was yet a boy, I saw you in Lower Asia with Polycarp, distinguishing yourself in the royal court, and endeavouring to gain his approbation. For I have a more vivid recollection of what occurred at that time than of recent events (inasmuch as the experiences of childhood, keeping pace with the growth of the soul, become incorporated with it); so that I can even describe the place where the blessed Polycarp used to sit and discourse — his going out, too, and his coming in — his general mode of life and personal appearance, together with the discourses which he delivered to the people; also how he would speak of his familiar intercourse with John, and with the rest of those who had seen the Lord; and how he would call their words to remembrance. Whatsoever things he had heard from them respecting the Lord, both with regard to His miracles and His teaching, Polycarp having thus received [information] from the eye-witnesses of the Word of life, would recount them all in harmony with the Scriptures. These things, through, God's mercy which was upon me, I then listened to attentively, and treasured them up not on paper, but in my heart; and I am continually, by God's grace, revolving these things accurately in my mind. And I can bear witness before God, that if that blessed and apostolic presbyter had heard any such thing, he would have cried out, and stopped his ears, exclaiming as he was wont to do: O good God, for what times have You reserved me, that I should endure these things? And he would have fled from the very spot where, sitting or standing, he had heard such words. This fact, too, can be made clear, from his Epistles which he dispatched, whether to the neighbouring Churches to confirm them, or to certain of the brethren, admonishing and exhorting them.
Did you catch that?
For, while I was yet a boy, I saw you in Lower Asia with Polycarp. And when was Peregrinus in Lower Asia? Prior to his going to Egypt. Yet Aulus Gellius writes:
When I was at Athens, I met a philosopher named Peregrinus, who was later surnamed Proteus, a man of dignity and fortitude, living in a hut outside the city.
And when was Gellius in Athens? In his youth. And with an estimated life from ca. 125 ad-185 ad, that would place Peregrinus right smack in Greece no later than 145 ad. Meaning that, either Irenaeus lived earlier than what we have presumed--which I don't believe--or, Polycarp is not Peregrinus; only Polycarp's martyrdom is based on Peregrinus's death.
Add everything together:
Agathobulus flourishing in Egypt early in Hadrian's reign
Gellius's account that he met Peregrinus when he studied in Athens in his youth
Lucian's testimony that twelve years elapsed between Peregrinus's initial criticism of the aqueduct and his death
Makes a 165 ad date for his death unlikely. The only way to make it likely is to accept that Lucian was fudging his narrative.