Well I've read the rules twice and still haven't solved the game yet. Here are my current thoughts.
One question is whether Omegon should reveal; the other is whether Legionaries should reveal.
An immediate Omegon reveal is clearly a high-risk/high-reward play, as it grants us a trusted civ who can also report their results. The counterplay is for the mafia to use these results to try to find Sheed; once they do, as we all know, we only have 1 lynch left before it's game over. On that note, they might not want to report their results, as each legionarie they find will narrow the list of potential Sheeds.
Is there any point at all when Omegon should reveal? Perhaps if they find Ingo, it would be worth it. At this point, town would lynch Ingo which harrows Omegon, but that's fine because Omegon has revealed already. If the mafia find Sheed, then Alpharius gets harrowed, and Omegon potentially has enough information to find Alpharius.
If Omegon finds Alpharius, well, it's roughly 50/50 as to whether this is the true Alpharius or a framed civ, so I wouldn't chance it. Although, if a Legionaire gets an Alpharius result, should that result be revealed? It would enable Omegon to safely claim an Alpharius result if they happened to target Alpharius that night, but the more likely scenario is that Omegon targeted someone else. Thus, we would most likely reveal a Legionarie for no reason other than two confirm two civs (the Legionarie and their target). Of course, mafia can fake claim a Legionarie result, or even fake claim Omegon, and that can be counterclaimed, but who to trust... things get quite complicated quickly.
There's the option of every Legionarie revealing every target every round, and trying to find the scum because they wouldn't be able to produce true claims, but I think this is a fool's errand, as we would be equally likely to find and lynch our own power roles.
Should anyone reveal anything ever? Well, at minimum, we should probably go all-out at Lylo. But most likely, we won't know what that point is, as mafia can end the game unexpectedly by lynching the remaining power role.
For now, I'm leaning towards holding off on reveals tomorrow. Although if someone is about to be lynched, they should probably reveal whatever information they have. If a power role (Omegon/Sheed) is about to be lynched, they should probably let us know they're a power role so we can choose someone else? Only problem is that the scum can pull this same tactic, so I'm not sure.