Akumura has no reason to try and stop us because even if Sabrina is shard of LoC, she does EXACTLY what Akumura would've wanted - keeps Madoka the hell away from Godhood, from all mystical bullshit for that matter really. I am racking my brain trying to come up with explanation WHY Akumura would do all these pointless hide and seek instead of just strolling up to Sabrina and teaming up officially or just taking hands off approach and let us do our thing. LoC on other hand... Look, Madokami is a bit stubborn ok? She might still believe that LoC is better solution than anything we could come up with and if Akumura split LoC into its own entity, well, this thing might not even be Madoka anymore in any capacity. LoC however tried to reconnect to Madoka first opportunity its got so it might still look for her.
So, there's a bit less logic to it.
Which could support a half-mad fragment or affiliate tasked with grabbing . . . Something.
And, thinking about it, even assuming that there's still some Madoka in the LoC at this point, it's dubious if we can say that it's really her.
Same goes for Homucifer.
We should treat PMAS Madoka and Homura as distinct entities from their divine counterparts. They may have had similar origins, but what happened has deviated a lot from canon.
(Same can likely be said of Sayaka and Mami, by the way)
Edit: On the whole "Is the LoC really Madoka?" thing, there's quite a few things that support that she isn't. Namely, being a god.
And some of her actions seem dubious. Like assimilating all her alternate versions, who had little to do with this besides being "related" to her, and leaving Homura behind. Granted, we're not sure how much of this she had control over, but it's something to note.
And we're not actually sure what happens to the souls she collects. We assume it's a magical girl heaven of sorts, but we don't know what that entails.
While we have less info on Homucifer, but "extreme emotional distress from Incubator field" and "becoming a god" definitely count for something.
So, you could probably argue about wether Madokami and Homucifer really count as Madoka and Homura. It's a Ship of Theseus problem, I suppose.
But we definitely should treat them differently from PMAS Madoka and Homura. They're related, perhaps even affiliates or fragments, but putting them into the same person box is inaccurate and will only lead to problems.
Edit: And, depending on how they're organized, treating all of the LoC as one person could be inaccurate. Same can go for Homucifer.