Isn't the comparative lack of infighting the Abomination's main advantage over Chaos as a whole?
There's very little passive infighting, but if an Abomination polity descended from the Imperium and an Abomination polity descended from xenos meet they'll fight.
Similarly not all abomination polities descended from the imperium answer to a central authority, they all believe that they are the legitimate successors of the Imperium, though some might have philosophies accepting all who follow a specific set of traditions as legitimate successors of the Imperium.
And the ones that follow different authorities and traditions can fight.
Vertical infighting doesn't happen, but horizontal infighting does. That is, a minion won't disobey his boss, but he will stab his equal.
The Angyls care only that tradition and authority are obeyed, and that those who deviate from one's tradition and authority are hated, feared and met with intolerance.
The cultists and followers care about which traditions and authorities are obeyed, and can have social movements that make preexisting traditions more widespread or more violently intolerant towards other subdivisions of the group.
For example, there was that time during the age of the Imperium that a forge world thought they could predict the future in the fluctuations of the astronomicon, gathered a bunch of other groups to believe that, then predicted that the Mechanicus and Ecclesiarchy were destined to merge into one organization etc. etc. Good stuff happens to humanity.
The Ecclesiarchy didn't like that and declared them rebels. A case of two authoritarian traditions coming into conflict.
Abomination polities will never betray their leaders, and might restrict undercutting their rivals to non-Chaos levels through tradition, but when they contain multiple supreme authorities, and multiple all important traditions, and those things come into conflict after previously being aligned they are sure to collapse into a war between what is now essentially separate nations.
I don't think we or anyone other than the eldar are likely to ever manage that on purpose, if it would result in a crippling civil war pragmatic cultists on both sides will work against the possibility, but if it involves purging a minority, then maybe.
Even if that minority keeps all the most useful tech hostage, it then becomes a question of practicality versus principle, and I think the Ophelian theocracy would fall heavily on the side of principle, betting on absolute commands to tech lower ranking captured techpriests to maintain their tech base.
If they even bother thinking beyond their hatred.
The other subtle alternative is somthing that doesn't rely on them being more focused on intolerance than practical gain, and instead relies on them being more focused on tradition than understanding in technology.
Allow me to explain:
If the Ophelians have a habit of stealing or reverse engineering Callamus tech Callamus could implant shutoff systems, or systems designed to subvert and shut off other Imperial tech into their design blueprints, so that when captured stuff is employed by the enemy they are subverting their own systems.
Or they could find/make a tradition, influence building, and proselytizing obsessed group of tech priests that're at a higher tech level than the Ophelians, but who have secret subversion systems in their stuff, and manipulate events such as to make them the dominant group of techpriests in the Theocracy after they become corrupted.
Then after getting this plan setup for hundreds of years they launch a massive campaign to take advantage of these created weaknesses.
The only problem, aside from the much weakened but still fanatical military opposition is that the campaign would be across an unprecedented number of tainted worlds, and attrition might well destroy their armies.
I am firmly convinced that Callamus can beat the Ophelian Theocracy with the right type of long con, taking advantage of inferior social systems around technology. I'm actually more worried about their other neighbors.
Edit, actually Callumus could pay the eldar to help manipulate and topple the Theocracy. That might make it much faster, within a single lifetime with juvenat.