We don't own a majority of it, AFAIK, and we control it even less than that. The fact that a noble owns part of it is irrelevant
There is no separation of the public and private sectors, if you think they could somehow ignore us. It's a holistic mass that works based on the directions of the people at the top, who are us and our fellow former government official Wilhelmina and her heir and our apprentice Eike, our other fellow current government official Baron Anton, and a gaggle of Stirlandian nobles who get to sit quietly and reap the almost supernaturally bountiful fruits of the opportunities we toss as them as long as they stay smart about it.
"Mathilde only owns a third of the EIC" is the sort of paper mache excuse that doesn't even fool our business rivals, who had to spend a few months quietly inquiring with us if trying to out-trade us wasn't going to end with us putting a horse's head in their beds or causing them to dramatically and mysteriously disappear with a faint but echoing screaming noise in the middle of their dinners.
The EIC is a trading company, divorced from the government in the vast majority of ways.
What do you think the government of the Empire is?
It's not elected bureaucrats. It's nobility. Hereditary bureaucrats. All the higher bureaucratic positions are just hats the nobility wears. Even the Elector Counts are just kings with a vote for who gets to be the king of the kings. The Elector Counts don't have a separate stable of incorruptible people, they just have their local nobles they know personally who they hope do what they say. For Stirland, that's us -- we're on a first name basis with Roswita, and we know a lot of the other people she knows and they know us too.
We are also a wizard lord. A lord of the wizards. That's not a high society aesthetic, it's a position where we can pass judgement over life and death, enact new wizard laws, and create new wizard offices and initiatives. As a wizard lord, we are the one who created the modern waystone initiative. As the one who created the modern waystone initiative, we are the highest human expert on the matter in all the Empire (and a solid +44 is pretty nuts to roll about it).
We are not the one the Emperor asks to choose somebody to manage any other waystone initiatives. That is because that question is not a question the Emperor is expected to choose somebody to find an answer for. It is our responsibility from top to bottom.
If the duty was given to an Elector Count, it'd be given to one with a clear track record against the forces of evil and excess resources to help with it, and who knows the most people involved with the magical side of things, and who also can't maneuver out of having to do the extra work. That's Roswita. She'd turn to her local nobles and choose from them the one with the most loyalty, boats, and magical expertise. That's us, Dame Mathilde Weber.
As a magical matter it's staying in the colleges, though, and that means with us, LM Mathilde Weber. Nobody outside the colleges even has the eyeballs to see the thing they'd be making decisions about. Nobody inside the colleges is yet willing to step on our murdery toes about it.