While scholars like Tov and Skehan argue for the originality of the Tetragrammaton their views are far from universally accepted. Their conclusions rely heavily on the limited evidence of fragments like P. Fouad 266.
Emanuel Tov and Patrick Skehan argued that Yaho was the original form of the divine name in the LXX, not YHWH or kyrios. They argued this on the basis of the good Septuagintal quality of the fragment containing Yaho in Leviticus (not P. Fouad 266) and the widespread use of Yaho in onomastica. To this can be added references to the normative use of Yaho among Jews and Christians by early Christian and Roman authors. You are correct there is evidence of diversity in the early LXX as argued by Frank Shaw and now also Anthony Meyer and others. Nevertheless, Tov and Skehan argued that Yaho was original and kyrios was a later form and Larry Hurtado latterly supported the view that kyrios only appeared in the LXX from the second century CE onwards.
Philo does refer to the divine name on the forehead of the high priest, knowledge of which some have argued he derived from copies of the LXX text.
There is evidence in the NT text of disruption around the use of the divine name in the high number of textual variants for kyrios and theos where the divine name originally appeared. This formed a key part of George Howard’s argument for the divine name in the NT, which other scholars such as Lloyd Gaston, David Trobisch, Frank Shaw, Luise Schottroff, and John McRay have supported. If the divine name did not appear in the original NT then is there an alternative explanation for the number of variants? The removal of the divine name also introduced ambiguity around the meaning of kyrios in texts such as Acts 1.24, 1 Cor 2.16 and Jude 5. Thus the original use of the divine name in the NT text resolves a number of problems including the persistent references to Yaho in various sources, textual variants in the NT text, and extraneous ambiguity surrounding the use of kyrios in various passages.