I agree that it’s a compelling speculation. I don’t remember the location of his comment, but I recall that Shadal rejects your speculation that the Christians were identified as Edom because many of the original Christians were Idumeans. He says that the fact is that the early Christians were primarily Jews, not Idumeans.

However, this is a little bit of “my guess is as good as yours,” and without examining the evidence thoroughly, even though he is certainly correct that the Christians were Jews, I don’t think your suggestion can be dismissed so simply. We tend to forget that at the dawn of Christianity there *were* Edomites.

1 – Herod the Great Murderer, who brought Rome into our area of the world – with the massive oppression and killing of tens/hundreds of thousands and the destruction that brought in its wake – was descended from a forced Edomite convert, and the fact of that heritage seems to have played a major role in the personal motivational forces underlying Herod’s actions (I believe “chazal” were fully aware that this connection was purely associative, since from Berakhot 28 and elsewhere it seems that Sennacherib’s confusing all national identities was accepted as fact universally; even Rabban Gamliel who disagreed there about the Ammonite convert did so only on the basis of his understanding that the Ammonites had reassembled and reestablished their national/genealogical/ethnic identity, but this was only after their earlier dispersion).

2 – I believe it is not unreasonably speculative to suggest that many early Christians were descended of these same forced Edomite converts. They lived close to the Land of Israel, and many were likely to have been put into (lower-level, local) positions of power by Herod and his supporters, thus growing numerically among the Jews of Israel. On the one hand, they had imbibed Jewish beliefs. On the other hand, they likely still held to pagan beliefs, that we know ultimately became part of basic Christian belief. Furthermore as insiders/outsiders whose Jewish legitimacy was questioned/questionable, and as representatives of a hated regime, it is likely that considerable mutual animosity reigned between them and “born Jews”. Moreover, they were likely seriously conflicted about their own Jewishness/Judaism. Thus, upon the destruction of the Bet Hamikdash and following the Roman oppression subsequent to the suppression of the Bar Kokhva uprising, these descendants of Edomite forced converts may have been at the forefront of those advancing the notion that G-d had rejected Jews and Judaism, reenforcing Jewish despair. Yet they were unable to return to the crude paganism their ancestors had known before their forced conversion, nor could they identify with the thoroughly corrupt and immoral leadership of pagan Rome. This complex may have made a major contribution to the formation of early Christianity (so little is known with certainty about the general population that became the base for early Christianity, that I believe these speculations as reasonable as others that I have seen, and I believe chazal’s identification of Christianity with Edom reinforces these speculations. I regret that I have not the time to record here or elsewhere more details elaborating and supporting these speculations). When the Christianity advanced by these descendants of forced Edomite converts became the official religion of the Roman empire, the association between Edom, Rome and Christianity became firmly established.

The above, fleshed out in more detail, seems so clear to me that it is difficult for me to understand why I have not been able to find it “in the literature” on the subject.