I'd probably take a lot inspiration from Warhammer Fantasy:
-There are several (Much smaller) Human states which are not as bad as the Imperium, who survive by dint of treaty, being too inconveniently placed, or other strategic concerns. Do not make them all secular democracies who are all totally fine with aliens and such-some of them will be monarchies, military dictatorships, theocracies, etc and some will be xenophobic too. They will be flawed, but still better than the Imperium-making any of them pure good guy faction would be boring.
I don't particularly care much about the Wargame (In fact I think it's kinda bad), but definitely make one of these factions a Tabletop faction (Also make the Wargame not suck)
-For that matter, make other human and Xenos Gods whom are not Chaos. Make the Imperium's strict monotheism actually matter by letting there be other options. Take inspiration from Warhammer Fantasy-these gods have to also actively intervene and actually matter-maybe make it clear that the Emperor (and by extension, the Omnisiah) is only the most powerful of the Gods of Man.
Actually, i'd also make at least one of those minor states still worship the Emperor (Or possibly Omnisiah), and show that it's possible to do so and not be fascist assholes.
-More Xenos, some of whom are not huge pricks, some of whom might be actually allied with those minor human factions.
-The Imperium...basically keep it as it currently is, except make it more clear that it is a failure state for what an Interstellar Human Empire should be. Maybe over time let it have "Character development" and start to soften it's stance on Xenos and "Pagans" (Those other god's worshippers) as part of larger storylines. Or maybe the opposite.
I'd keep the heroic characters within the Imperium that are prevelent within the Novels, but make it clear they're either powerless to really change things (Either literally, or as a matter of mindset), make them eventually rebel, become attempted reformers, or have them eventually become villain protagonists. Also have at least one novel series about Rebels against the Imperium that doesn't have them be Chaos cultists or evil. Whether they succeed, all die horribly, or something else is open though.
All of the above also applies to the Mechanicus, and all other Imperial Institutions.
-Chaos.....keep it as is in general concept, but make it possible to be redeemed and purified. Not to a Star Warsy extent, but definitely make sure it's a possibility.
Also, add various minor Chaos Gods. None benevolent, but perhaps not as rabidly destructive as the "Big Four". Or sometimes more, such as Malal.