I get what you mean when you talk about an MC in the OS, but because I know it will come up, let's get it out of the way. There is no MC in the OS throughline. There is a character/player that is your MC character that also has a role within the OS. Because it's two different roles and two different perspectives, I think it's probably okay if this player acts differently depending on which throughline they're representing at the moment (though i'm interested in how others see this because i really don't know if that's accurate).
That's how I'm seeing it. As a linear problem solver, if i find out that someone else is getting paid more than I am to do the same job, and they have no more seniority than I do, I will absolutely let that imbalance/unfairness be the source of a problem for me. From there, though, i can attack the problem by taking a straight, linear path, or I can attack it by determining how things need to be balanced.
What I'm getting at, i think, is that we need to keep the problem of balance separate from a problem-solving method of looking for balance.
Awesome! I love ghost stories!
So your original question (Any advice on how to approach the storytelling so that the MC's reasoning in maintaining a particular inequity in the OS seems sufficiently linear?) asks about linear reasoning for the player representing Inequity. I don't know that I could speak to reasoning, exactly, since I'm arguing that linear and holistic are approaches to problem solving rather than reasoning for problem solving, if that makes sense. But to keep your Inequity player firmly rooted in Linear problem solving, I think it is just a matter of what they do to keep that inequity there.
Without knowing the entirety of your story, i'll suggest that disrupting the seance or destroying the magical artifact that would bring her back seem like very linear approaches to me. Or maybe refusing to sign, or somehow destroying the contract could be linear ways to maintain this particular inequity.
I'm not sure I could counter with a Holistic approach just to show an example of the difference because i'm not a very Holistic minded person, but I'd be interested to see you or others offer a holistic approach to maintaining this particular inequity.
Anyway, is any of that helpful? I'm still hoping others will jump in, too, just to get another view on all of it.