I disagree about your use of “unbiased.” History is full of bias, and witnesses always have a bias in their view. History is not recorded in a lab with careful controls. However, you are at least as biased as those men were. Here you reflect your own anti-constantinian view and use that to disqualify the writings of people 1700 years closer to an event than you are as to what that event was. And I think your view of Constantine is unfounded. Nothing that I have read has ever established that he promoted a view of the Church established on authority in Old Rome. He may have supported it, but since he moved his seat from that city to Constantinople, and since that city very early on began arguing in the Councils for her own status, it certainly seems unlikely. If anything he would more likely be in support of New Rome not Old Rome.
I also think you make a switch in the above argument, from whether St. Linus was the first bishop of Rome to a general discussion of Papal primacy. Your list of six would more than likely relate only to the former than the latter. You seem to be starting with that specific topic and then generalizing your understanding and applying it to the whole tradition of the Papacy. They are not the same issue though. I think there is a very strong assortment of Fathers, councils and such for Roman primacy thoughout the Early Church period, including Igantius of Antioch if I recall correctly as well as Iranaeus again, and very few probably discussed St. Linus. Even the Eastern Churches universally accepted the primacy of Rome, though they argued about just what it entailed.
But, again, you have not demonstrated that he manipulated history for Rome over any other Church. Neither have you demonstrated that Constantine held such a position, and that is the entire keystone of this argument.
Yes he wanted orthodoxy, but you have not made a case that he selected what was orthodox. All indications seem to be that bishops, in council, decided that and Constantine accepted it and promulgated their decision with his authority. If you are saying that he determined what was orthodox then you would have to support that with something, and nobody else as ever seemed able to do so.
You have not established this though. Is it your bias about the “controversial” emperor, or is it real bias on the part of Eusebius? Eusebius is an excellent historical source very close to the periods we are discussing. Throwing him aside would be akin to ignoring Suetonius regarding the life of Caligula. And again the only thing you are casting doubt on here is whether it was St. Linus or St. Clement who succeeded to the papacy in Rome. That is an historical curiosity of some merit, but it hardly makes a case as to whether Rome had a primacy in the Early Church, which is certainly well attested.
I don’t see that at all. Whether Rome’s primacy was one of universal juridical authority or some other form is certainly arguable, but not that it had primacy. That has tremendously strong beginnings.