Do you agree with Madness that perhaps Big Moe just let Kellhus yammer on about discrepancies in voices while in truth the Cish easily rooted out the skin-spies?
Well, even Kellhus temper's his conjecture there:
Then, about twelve years ago, you discovered the first of the Consult skin-spies—probably through discrepancies in their voices.
I don't think Kellhus really fully understands the Third Sight at this point (in fact, he might never really, since he couldn't ever experience it himself).
I think in line with what you are saying here is that what the Cish see has, to them, always correlated with souls. They perhaps see souls as entities with passions, intellect, etc. And before they never had reason to doubt this correlation.
Perhaps it's also the case that because they felt they could still see "souls" in the skin-spies they insisted that these were not biological machinery but magical artifacts made by the Scarlet Spires?
Well, I think that the Cishaurim leadership likely already had "reason" to suspect or be worried about the Scarlet Spires. The only other group they'd likely suspect more would be the Imperial Saik and they likely had little reason to think they could pull off such a feat, simply because the Diamos is far more mysterious, in-world, as to what it might be able to do. Being so beyond what the "usual" Anagogis could do, they are likely right in worrying about if it could well pull a soul
from something.
In the end, I suspect this actually is a slight plot hole, but one easily hand-waved away. It was the case that pre-"twelve years ago" the Consult rarely had reason to install skin-spies in Fanim lands, so there wasn't really much reason for concern by either party. When Moe arrives though, his curiosity and general thoroughness means removal reaches a fever pitch, raising things to a new level for both the Cishaurim and the Consult.