I don't mean to continue a debate which I originally behaved deplorably but don't you agree that at least some of these texts come from different Christian communities? To that end, I think we should qualify your initial statement to the closest fit for each:
The epistles of Paul (authentic epistles) = Philo of Alexandria not the DSS cf. especially H. CHADWICK, 'St. Paul and Philo of Alexandria', BJRL 48 (1966) 286-30
the Didache = DSS
the gospels = it depends if Secret Mark is acknowledged to be authentic or not
To me that saws the balance in half. Secret Mark - or if you prefer more broadly - Clement's Alexandrian community's gospel is more Philonic than it is 'Qumranic.' Agree or disagree? I think the issue here is an assumption of monolithic 'Christian origins' for all communities. That the Marcionites argued that the New Testament was 'Judaized' clearly extends to the Pauline epistles. Where there are interpolations they inevitably are 'Judaized' interpolations or interpolations which make Paul sound or adhere to pro-Jewish, pro-Jerusalem, pro-Pentateuch, pro-prophetic conceptions.
As I have said before Irenaeus/Tertullian consistently argue against the mystery religion origin for Christianity. This is evidenced in Against Heresies, Against Marcion, Prescription Against the Heresies among other Irenaean works. The argument must be clearly delineated to at least consider an alternative model for Christian origins.
At it's core the idea from 'the heresies' seems to go something like this. 'The apostle' identified as Paul and the author of both the ur-gospel and 'Apostolic' writings by the heresies somehow inferred that he had written a 'secret gospel' based on certain passages especially 1 Corinthians 2:8ff. Looking at this section of Corinthians the idea seems to be that Paul submitted one gospel to everyone and reserved a secret gospel for the elect. This dovetails well with Clement's understanding of Mark writing one gospel according to Peter and another 'secret' gospel with his own mystery-based religion added to that 'simple' gospel of faith. Paul of course is not Mark. That is a difficulty. But the parallels are real and not easily dismissed.
It seems to suggest to me at least that 'the apostle' whether called Paul or Mark founded a mystery religion at Alexandria where - among other things - Clement says "he yet did not divulge the things not to be uttered, nor did he write down the hierophantic teaching of the Lord, but to the stories already written he added yet others and, moreover, brought in certain sayings of which he knew the interpretation would, as a mystagogue, lead the hearers into the innermost sanctuary of that truth hidden by seven veils. Thus, in sum, he prepared matters, neither grudgingly nor incautiously, in my opinion, and, dying, he left his composition to the church in Alexandria, where it even yet is most carefully guarded, being read only to those who are being initiated into the great mysteries." The same idea is present in Refutations alternative understanding of Marcion's use of the gospel of Mark where certain 'mystical' sayings of Empedocles are 'added' to canonical Mark.
I would argue that given the context of Clement of Alexandria as one who used both the secret gospel and the mysteries referenced in the discussion of its authorship that Clement's reliance on Philo and his discussion of certain gospel passages shows an uncanny interplay - thus explaining the Philonic origins of this specific (and admittedly secondary) development within Christianity. Of course if secret Mark was more original than canonical Mark and Clement simply developed the story as a way of explaining and justifying its existence then Christianity beginning as a mystery religion also has possibilities.