Thanks for the thought out response (absolutely no sarcasm intended. I just like being able to say something, and getting a response to what I actually said! Strangest thing!)
1- I didn’t know that a murder is reburied. But I looked into it, and that which you say (was this your source?) is a Gemara in Sanhedrin, 47b, explaining that the Kapara of the Daled Misos Beis Din is only after his execution and the rotting of the of his corpse, hence, after the Ikul HaBasar, his body is returned to Kivrey Avosav, because Kapara is complete.
A suicide, I would propose, doesn’t have the intrinsic Kapara of his actual death being a Kapara, as it was an Averah unto itself, nor the rotting of his corpse, as by the Daled Misos it would seem to be an extension of his execution. By a suicide, that too would not be a Kapara. Hence, the suicide’s corpse would remain eternally chutz Lamachaneh.
But not because his chet is intrinsically worse, but rather because the same Kapara is not available to him. The litmus test for this would be the following – say someone is dies a natural death, and only then we find two witnesses who reliably accuse him of murder, would we move his body? That’s a question unto itself; I know of no source for postmortem punishment from this world, one could presume that after death all punishment is given to the Beis Din Shel Maalah and we’d have to ask ourselves if being buried out of the regular graveyard is a punishment, or merely due to to the honor of the others buried there? I presume it’s the latter, as you pointed out.
2- But I assume that someone whom we know reliably (I wonder what level would be required) committed murder would not be buried in Jewish cemetery, much like anyone else who was not Shomer the Taryag Mitzvos. Source?
3- As far as losing his chelek of Olam HaBah, we do not find a suicide listed in the Mishnah in the beginning of Perek Chelek where those who have no chelek in Olam HaBah are listed. I later found that the Yad HaMelech on Rambam (when the Rambam speaks of a suicide, and the fact he receives no honor in burial) actually says that he heard the same thing! And he looked everywhere, and couldn’t find a source. He quotes the Maharit who assumed that this was true, but he rejects it as being sourceless! He even brings a proof to the opposite effect, that Achitofel (who killed himself) is listed as having no chelek l’olam habah. And the gemara explains that this was because he was Malbin Pney Chavero b’Rabim. Asks the Yad HaMelech, why doesn’t the egmara says that the reason was because he committed suicide? Hence, it must be that after the kapara for such a horrible chet in gehenom, he could have indeed have had a chelek l’olam habah!
As far as Josephus, as a historian he is relied upon (we find Tosfos and the Rishonim do quote him). He had a very chashuv brother (points for guessing who). Interesting. That requires thought.