The main thing I rely on is the Synoptic Gospels much earlier dating (which has added weight in light of the scholarly consensus they were not themselves original, but products of the even earlier lost Q text.) It was not just a PR war, after all; the Synoptic Gospels and Pauline school with which they are consistent were better established and more pervasive because they had been around longer. That is not in itself conclusive, no, but does give the Synoptic Gospels closer proximity to Christ Himself, and the closer they are to the Source the more unassailable they become.

So when hidden Gnostic gospels came along they naturally ran afoul of the established Church. Fans of heterodoxy as an end in itself consider that a badge of honor, but fighting a vast conspiracy loses its nobility if the conspiracy is just an empty allegation contrived to legitimize ones own agenda. Opposing a conspiracy revealed by a pattern of anti-Christian behavior and doctrine is one thing, but opposing the established Church simply because it disagrees with some novel personal warping of Christian doctrine is quite another. The Church did not reject Mormonism because it had something personal against Joseph Smith or was jealously guarding its temporal power, but because he made up a entire new doctrine out of wholecloth and tried to promote it as "real" Christianity.

Of course the early Church was consistent with the Synoptic and Johanine Gospels, for the very compelling reason they provided its best and earliest understanding of the Rock on which the Church was founded. Even by generous estimates they had already shaped Church doctrine for at least a generation before any Gnostic "Gospels" existed, and not as an overt Gnostic attempt to coopt Christianity as it was systematically doing with all other religions. The Church long and largely dependent on the former to the exclusion of the latter inevitably ACCEPTED the former to the exclusion of the latter, even if it did not formally do so until the end of the Fourth Century. That is not conclusive, but is corroborative.

It is a case of convention reflecting chronology and therefore increasing its significance, but the chronology and distinction are what I find most convincing. The Christianity of the Gospels is not another generic mystery religion, and was recorded in them well before the end of the First Century. In skimming Wikipedia articles on the subject I ran across a quote from a scholar noting that none of the canonical Gospels mentions the destruction of Herods Temple in 70 AD, despite several mentions of Christs prophecy it would be torn down until no stone stood upon another. Obviously any author would want to include clear fulfilment of explicit prophecy, and the canonical authors routinely did; omitting that one strongly suggests its fulfilment is absent because it had not yet occurred.

That places all the canonical Gospels at or before 70 AD, meaning they were accepted as, well, GOSPEL, decades (if not a century) before the Gnostic alternatives existed. That makes it very hard to accept any later writings not fully consistent with them and the early Church so tightly bound to them. The gnostic writings conflict with so many of the Church Fathers is, again, not conclusive, but underscores the conflict between gnostic texts and the canonical ones dating from a time and authors much closer to Christ Himself.