I agree that if your interest is in historical reconstruction, it is not fruitful to accept literary sources at face value; the voice of the author must be distinguished from that of any persons represented in his narrative, such that the very different "voices" of Jesus in the various gospels reflect to a great extent the different views and creative expression of the gospels' writers. The gospels moreover are not straightforward biographies or historiographies; they devote a great deal of narrative to interpreting the meaning of Jesus on account of what is written in the OT.
But once you start to reconstruct the "historical Jesus" from what is written in the gospels, whatever "Jesus" you come up with depends entirely on your own subjective presuppositions and procedures for sifting through the documentary evidence. One could have criteria that assumes that the gospels are mostly accurate or one could have criteria that leaves very little for historical reconstruction. The most hazardous and speculative part of this enterprise is reconstructing Jesus' assessment of himself. It is just not possible to discern Jesus' mental state and whatever he is reported as saying in the gospels is filtered through (or created by) the writers' own religious views and creativity. So to claim that Jesus never claimed to be a messiah imo goes beyond the evidence. This is different from claiming that it cannot be determined whether Jesus claimed to be a messiah.
What is more helpful is to examine what first-century Jews actually believed and expected (as it is meaningless to say that the Jews were expecting the Messiah) and then compare how well the gospel portraits of Jesus fit into these messianic paradigms. The reality is that there was a wide continuum of ideas: some expected a Davidic king to restore Judean sovereignty, some expected a heavenly figure to arrive who would bring about divine judgment and God's rulership, some expected a priestly figure to reform the corrupted Temple cult and restore God's favor on Israel, some expected a prophet foretold by Moses who would bring out righteousness by giving the definitive interpretation of the Torah, some expected a figure or figures whose death(s) would bring about redemption for the Jewish nation, some even expected a Gentile messiah who would be appointed to rule the world. For a detailed exploration of these views, see George Nickelsburg's Ancient Judaism and Christian Origins: Diversity, Continuity, and Transformation. The Christian view of Jesus as the Christ combines features of many of these expected figures into a single individual (in the NT, Jesus is seen sometimes in Davidic terms, sometimes in priestly terms, sometimes as the heavenly Son of Man figure, sometimes as a Moses figure who gives the Torah its definitive interpretation, sometimes as a Suffering Servant figure whose death brings salvation to those who believe in him, etc.). It does not seem likely that the historical Jesus (accepting majority opinion on this matter) claimed to be the realization of all these different messianic ideas, and there is no firm evidence outside of the gospels that he made any messianic claim, but it is also not improbable that he did claim something about himself that reflected religious expectations; Josephus mentions many who did so at the same, who sometimes met gruesome ends at the hands of the Roman authorities. If anything at all in the Jesus tradition is historical, it has to be that Jesus was crucified (the one thing mentioned throughout all Christian tradition), and this would indicate that he was put death for sedition (as also the charge "king of the Jews" implies). The fact, while far from conclusive, imo makes the possibility more likely than if we only had Jesus' statements in the gospels to go on. But this is quite different than later christological ideas of Jesus as the Christ.