While waiting for GURPS Conspiracies . . .

[Curmudgeon]

Nice summary.
I'd pretty much agree with it, except that my calculations assuimed they'd be willing to devote as much of their weekend time as did of their weekday time. In effect, conspiracies don't take their weekends off, for purposes of determing "free help" available. Also, to avoid confusion, I was using agents only for full-time membersof the conspiracy (the ones who get paid the average income ), in effect the conspiracy is their day job. I was using members for anyone else who belongs to the conspiracy but doesn't have it as their day job. But other than that, an admirable summary.
As to other factiors affecting the effectiveness of a given conspiracy, I would think that a factionalized conspiracy would be less effective than a similar-sized conspiracy with the same resources that didn't have members with other agendas to deal with.
I see a factionalized conspiracy as wasting much of its resources, including time, on in-fighting over the proper methods and goal of their conspiracy.
To some extent, I would look at defining the city-states, or at least the conspiracies, in Aether, according to the social parameters that GURPS Traveller: First In used for planetary cultures. The eight axes would be: Pluralism-Monolithic (pluralism); Cordial-Xenophobic (toleration); Collectivist-Egoistic (solidarity); Submissive-Rebellious (tractability); Violent-Pacific (aggression); Empirical-Mystical (pragmatism); Progressive-Reactionary (innovation); and Prudent-Reckless (providence). You can eliminate any axis that doesn't seem particularly useful/relevant according to your needs.
A empirical (highly pragmatic)-prudent (highly provident) conspiracy would assume as a matter of course that every city-state has a conspiracy and that all of those conspiracies are actively working against their conspiracy, even if it's not actually true, just because they wouldn't regard it as wise to assume otherwise. Being pragmatic, they'd downgrade threats that didn't seem inimical to their interests and they might even work with another conspiracy on a common project, once another conspiracy was found and investigated, but they'd probably never take any conspiracy completely off their watched list and they'd always be watching for that expected dagger in the back. That kind of conspiracy could reasonably be expected to put more of its effort into weeding out spies in its own ranks and running counter-conspiracy operations at home more than into adventures abroad.
A monolithic-xenophobic city-state is going to be hard for any outsider to infiltrate. Any behaviour outside the expected norm (eating with the wrong fork or putting the fork on the wrong side of the plate or dressing differently) is likely to raise suspicion. Any conspiracy that has goals that run counter to those of it's city-state is going to be near-paranoid since it's in constant danger of being found out and it'll be looking at a very bad reaction to it. OTOH, a consiracy to further the aims and culture of the city-state could be an open secret because it has the full backing of the city-state, however discreet.
By the by, was the part about starting wealth helpful?