No, you’ve misunderstood. As I said before, Beckwith processes those patristic mentions. There is no contention that the books were individually written 4th Century. I didn’t say that, and Beckwith doesn’t say that. The contention is that their inclusion into any kind of canonical status didn’t happen First Century under the Jewish magisterium, but in the 4th Century, under ostensibly Christian scholarship. This precludes them from being part of the corpus of canonical text to which Paul was referring in his epistle to Timothy.
All that may be so; it is not then at least "absurd on its face" as I wrote. It is simply an irrelevant to the present dispute hypothesis.
This precludes them from being part of the corpus of canonical text to which Paul was referring in his epistle to Timothy.
Absolutely not. St. Paul was referring to a set of books coming from the Jewish tradition that are nevertheless inspired. Not canonical according to some false religion, but inspired by God. It is, remember the same Paul who corrected Peter for keeping kosher; what concern of his would have been, at the end of his life, what some group of rabbis decided about the books pious Jews wrote dreaming of Christ and freedom centuries prior, and which Christians knew and loved?