And Mark Havel, I think I like that idea best (although I see the logic in what others here have wrote). But your idea is so simple I'm ashamed I didn't think of it right away.
EDIT: Actually, now that I think about it, although that is a great idea, it falls into the same category and has the same pitfall for me of having two separate quest-lines with the same goal. Double the amount of work and double the amount of voice work that would be required. Generally that would not be so bad, except for the fact that I'd rather put most of my work into other events that I want to happen in the mod. Having two in-tandem quest-lines with the same goals from two different points of view would balloon my work-load to a state which I'd consider to be a tipping point for what all I could actually get done in a timely manner. Although I cannot deny how cool that scenario would be.
I think I'd be better served going with Darth's last suggestion of using a cover identity.
Unless someone can think of someone or some group with enough power to get a person (the Player) who would be considered an enemy (if they joined the Stormcloaks) assigned to the group? And honestly, even if there were such a power group, them pulling those kinds of strings, I imagine, would attract a lot of attention to the investigation/expedition. Which is not what I want, at least initially, when the expedition starts.