So, before I start thinking of something else, I might as well throw out some Ilba/Perdix possibilities and see what sticks. I'll start out with "premise nonsense", then "Perdix and Ilba nonsense", and then "larger scope nonsense", so skip at will by running "find" on those exact phrases. There's a picture of a pony at the end.
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GENERAL NONSENSE:

For my own purposes, I've been trying to establish the Monkeys as a kind of rudimentary, networked social religious sect that uses a kind of home-brewed magic as its main executionary force.

As I've established so far without being smacked, Monkey magic is much more limited in scope than Cholaeic magic (all it can do is balance social elements), but also much less rigid about the separation between individuals. Thusly you can raise an army of Monkey minions who spend most of their time being normal men, but who can become a collective force when switched on. Likewise you can have a big network of creepy witch-women.

You can also have an intimate magical relationship between a King and Queen which ideally forces them to work together and share resources or face becoming impotent (King) and conspicuous (Queen). A standard-issue royal couple would look magically very similar to each other. It's sort of like the Clintons.

Because Ilba and her brother were twins, married, and shared a Gift, when examined through a Cholaeic lens, they would appear to be EXACTLY the same person inhabiting different bodies, and magical aptitude would be shared equally between them. If you had an arcane connection to Ilba's brother at the time and said something, she would've heard it as well.

Unlike the Brought To You By Cholaeic Magic Perdix, however, they were each able to maintain a distinct consciousness and separate social roles.

My impression is that, if the Ilba twins were separated for a long period of time, they would have become increasingly uncomfortable as their mutual protections degraded, and more and more of the magical onus would drift away from the brother and onto Ilba, who would then be a Roman candle in a darkened theater full of angry people wearing flammable outfits.

PERDIX AND ILBA NONSENSE:

So now brother is toast! Well-meaning but distracted dragon mages aside, Ilba would be utterly screwed if Monkey hadn't given Ilba what amounts to a shotgun civil union to Perdix. From my stance Perdix is now technically a sort of Viceroy to Ilba's Queen, thus dousing Ilba's glow and ensuring that nobody can utilize her without going through Perdix first - while neatly avoiding any of the marital or political requirements that would apply to a real marriage.

The downside to this is that we now have two distinct systems of magic chugging along side by side and screwing up the readings.

According to Ilba's system, the identity confusion is perfectly normal, and she CANNOT HELP but semi-consciously reinforce it for her own safety. She will do just about anything in order to maintain balance in her relationship with Perdix, and by extension, the balance IN Perdix.

Their current experiment is deeply disturbing because suddenly the power has punted over to Abakoshi, and their awarenesses are splicing. (For Ilba, more than one splice in a relationship is bad news). Ilba will stay with Shotik out of a ground-level belief that if she sticks around him long enough, he'll either:

(a) absorb half of her firepower, which ensures that Shotik will remain connected to her (maybe even more connected than currently), AND be less vulnerable

or

(b) by tilting the field to Shotik's side, a good portion of Abakoshi's power and mental connection will flow downhill and back into him, reestablishing parity.

Since Perdix is a Monkey like Ilba is a Derlethian - only on the tax paperwork - I doubt either of the above things will happen the way Ilba, in her subconscious lizard brain, hopes they might. However, I would like SOMETHING further to happen, because, fun.

It would be nice if Perdix and Ilba were to subtly cross-pollinate some of their milder respective aptitudes, so that they have to forcibly sit down and overcome their mutual startle response.

I do not want it to be in a traumatic vein, because I don't think trauma adds interest for them at this point. I would rather go for the "gradual yet meaningful awakening" angle, mixed with a few choice pratfalls. Soft focus. Vaseline on the lens. Etc.

LARGER SCOPE NONSENSE:

On the broader level, Nil has already pointed out (although to panicked ears) that several layers down, the Cholaeic analysis can identify the difference between the Perdices and Ilba - sort of on the same order as there's a legal difference between a native-born American citizen and a naturalized one. You can tell that Ilba is the "immigrant" party.

It would be more interesting to build some excitement about what appears to be a an active and peaceable merger between two very different magical systems. Can Monkey social magic be somehow extrapolated from its theocratic roots and reverse-engineered into a Cholaeic discipline, &c.

It would be very pleasing if the benefits of actively but carefully crossbreeding a small, easily killable apprentice - one who's so pre-imprinted that totally shaking her out probably won't work anyway - in a controlled, under-the-radar atmosphere could be talked into outweighing the WRONG WRONG WRONG kneejerk reaction.

Ilba and Perdix will be much more fun if they're both compromising on their comfort zones, rather than just Ilba getting deprogrammed and Perdix being huffy about it.

Monkey isn't stabbing her bosses in the back for nothing (nor just for Ilba's personal sake), and she shut down Sonata's bad PR fling so firmly for a reason; she has active and wide-ranging ambitions relating to the Cholaeic presence in Gaetan, and I would like to set this up as something which could have very tempting benefits for just about all of the mages in the covenant.

Except for Gi, because, horses and fairies, whatever.

And now, enjoy this pony.