Re: The Accession of Darius III
Yeah, Diodorus' account is garbled and very stereotypical, so I also lean towards the hypothesis that Artaxerxes III died from natural causes. He was quite aged in 338 BC (probably around his sixties), so it looks reasonable. As far as I know, the tablet does not specify the causes of his death, but the expression used "met his destiny" doesn't imply any wrongdoing. On the contrary, in the case of Xerxes' death, a Babylonian tablet (BM 32234) explicitly mentions that the Great King was murdered by his son. In my opinion, Diodorus duplicated the alleged circumstances of Arses' elimination, probably inspired from the extravagant stories already circulating about the supposedly atrocious demise of Artaxerxes III. Some of them are reported by Aelian and Suda, are even less credible than the passage of the Historical Library and may betray the Egyptian origins of the story.
That being said, I don't see why the existence of Bagoas should be denied. As you said, the contribution of a court dignitary in the overthrow of Arses is confirmed by an independent source and I don't see why he should not be identified with Bagoas. His role in the conspiracy was definitely distorted, in order to fit the literary tropes of malevolent eunuchs or present Darius in a positive light, but a court official was certainly involved and there is no reason to deny the claims of his name being Bagoas. Darius being the satrap of Armenia and marching to the capital (probably Susa) also sounds convincing, but his satrapal position is only attested by Justin, as the Dynastic Prophecy simply states that the pretender marched to the throne. In my opinion, disgruntled or ambitious officials may have taken advantage of the new monarch's still unconsolidated position to overthrow him. Darius revolted in one of the satrapies (Armenia? The Cadusians were near the region, but the story is legendary, although there might be a kernel of truth inside, like a battle between Persians and Cadusians, where Darius participated) and Bagoas plotted against Arses in the palace. Once Arses was out of the picture, Darius and Bagoas quarreled, the former prevailed and then tarnished the latter's reputation, in order to reinforce his legitimacy.
That being said, I don't see how the lack of documents dated under Darius could be interpreted as a sign of his dubious legitimacy. Contracts and correspondence were always dated under a specific monarch. The rarity of Darius' name's attestations is a result of not many tablets dating from his reign having been discovered, which is not that unreasonable, as we lack large corpora from that era, not to mention the fact that Darius' reign was rather brief. After all, murdering your predecessor or the legitimate heir was not that uncommon in Achaemenid history. That's how Darius I, Artaxerxes I, Sogdianus and Darius II gained the royal power. Finally, in regards to the alleged Babylonian rebellion, it probably never happened. The name of the rebel leader is Nidin-Bêl, which is essentially identical to that of Nidintu-Bêl, the first Babylonian rebel between the reigns of Bardiya and Darius I. My guess is that the scribe, writing under the Seleucids, made a clerical mistake, mixed up the two Darius and inserted Nidintu-Bêl before Darius III, instead of Darius I. The most serious trouble came from Egypt, where Khababash controlled Memphis and the delta, most probably in parallel with Arses' reign. His insurrection may have inadvertently helped the plans of the conspirators.