The empires (or associated entities, such as the Minmatar Elders) have been known to either circumvent or outright attack CONCORD when there are sufficient interests at stake.

Nation states, in dealing among themselves, exist in a state of anarchy. This is as true for interstellar empires as it would have been for a planetary nation. Complying with international law is more a matter of public relations and keeping on good terms with one's neighbors than of crime and punishment the way we normally think of it, and CONCORD is more mediator than police officer, where the empires are concerned.

Actually, this is pretty much the way capsuleers relate to one another, as well-- as mini nation states-- though in their case CONCORD is a little bit more of a force to be reckoned with.

... Inquisition? I ... do not think this word means quite what you seem to think.

Leaving that aside, there are many ways to play a neutral role-- notably, standing back and observing. The Sisters of Eve will be sending medical craft and supplies to both sides, for example. Most capsuleers will similarly take no side, busying themselves with their private affairs.

CONCORD will probably keep the peace for as long as it can, then stand back, cluck its tongue disapprovingly, and try to drag all concerned to some kind of truce as soon as anything that vaguely resembles a stalemate appears.

The interesting question is what the State will do. The Caldari don't approve of conquerors, generally (they tend to be willing to conquer more than just our enemies), but the Amarr are allies, however much some might wish it were otherwise. At most, I suspect that the State will continue its simmering conflict against the Gallente, and only involve itself to mirror and counteract Federal involvement. That, of course, could lead to quite a conflagration if the pattern escalates.

An important distinction that you seem to be missing is the one between "heretic" (offshoots of the Amarrian faith such as the Sani Sabik and EoM), which are likely to be killed where possible (they have, as I understand the logic goes, turned away from heaven's door once and cannot, therefore, gain entry)

Perhaps you see the Amarr as monstrous and our association with them as unconscionable, but you forget too soon and too easily. You have swallowed the individualists' bait, forgetting how fine and subtle the hook is, and they have dragged you to their side, jaalan. The Gallente are no more monsters than the Amarr, but their way of life is antithetical to ours, and they, unlike the Amarr, actively and presently seek our cultures' destruction.

You have been played.

What planets are you exactly speaking of? Your goals might conflict with the ones of Intaki Liberation Front.

No doubt there are economic considerations and such at play. You don't get to be a great power by being blindly idealistic. That said, I don't see much sign that the Amarr are exactly dependent on slave labor for all purposes. They use it, certainly, but theirs is not a society lacking underclasses or tradespeople.

Do the Matari strike you as being close to despair?

They are not going to back the State against the Empire, nor would they side with the Matari. Even if they did, the resulting power would be no puppet of ours, would have fewer qualms about hybridizing Amarrian technology with less antique forms, and would likely be back on its feet and seeking vengeance within a generation or two.

Lest we also forget, the State has the lowest population of any empire. The Amarr have the largest. We are not likely to be able to hold what we take.