Technique D) You compartmentalize as much as possible and keep the number of people aware of the secrets low.
This is another very useful technique employed by many different kinds of organizations. However, your organization is not interested in small schemes, it is interested in large plots that have proportionally sized rewards. So you face the same problem as every other organization that undertakes large engineering projects. No matter how you arrange matters or how many layers you create, you still end up with 1000's of employees around the world that know highly critical information. And it bears repeating that your employees in particular find betrayal to be an attractive prospect, unlike many of the other oragnizations that use this technique.
Technique E) You make use of kill-switches.
This certainly would put a large scare in your employees, but it has some fatal flaws that can not be corrected. First of all, having a network of kill-switches means that an interfering agency could potentially hijack this network and cause all of your employees to drop dead at a moment's notice. Additionally, what do you do about intentional / accidental faraday cages (planes, boats, certain buildings, etc.)? Do your employees die when they lose network connection? Or can your employees only be killed when they actively receive a network signal?
So, with all of the aforementioned techniques being insufficient, what is the only thing that can possibly let something like your organization survive? What is the "bare-minimum technique" or combination of techniques that attains the high degree of perfect secrecy you require? The bare minimum that could possibly achieve it is this : mind control. Or perhaps more appropriately identified, body control.
For your organization to survive, you require the ability to directly pre-empt your employee's attempts to betray you. Not simply hoping that they will never do so, or simply punishing after the fact, but actively preventing their body from communicating what is happening to outsiders AS they attempt to do so.
From the perspective of secrecy, this technique is almost perfect. And from the philosophical perspective, what is the ultimate betrayal you can experience in this physical world? The betrayal of your body to your soul - your body's disobediance towards carrying out your intentions. You have a mouth, but no permission to scream. A betrayal like this would be very consistent with your organization's beliefs.
So consider if your organization did have access to such a technique, what effects might it have on your other beliefs? Would you begin (or already) believe in some sort of collective consciousness, or perhaps the opposite of it, the collective body? Would you actively insult any force that you believe grants people free-will? Would you begin making your members engage in acts of extreme humilation or pain for your own pleasure? Would you attempt to create devices that can bring the same circumstances to outsiders of your organization?
But body control… that would have to be black magick. The best technological attempts at this in 2021 are neurological implants, and those are still under active development with very limited success. And your organization is over 100 years old! The ability to control people's bodies at any distance in the late 1800's would necessarily have to be spell-like in nature.
Phew, it settled then. It's a good thing organizations like this don't exist. That is to say, organizations that have an absurdly successful degree of secrecy, in which the only information about them comes from outsiders who accidentally collide with their secrets. Really, do you think you've ever seen any secret-society members, who somehow appear to be willing and unwilling to speak at the same time? Who appear to be cringing at their own actions right as they do them? Thankfully we do not, because what would be your responsiblities if you became aware of such a person? Even if you sought to treat such a person with kindness, What actions would be necessary to treat this person mercifully? It's just a silly proposition, like having to invite vampires into your own home.