So, rather than
"Eike Study: Investigate (one of the isolationist houses), with an eye to learning about the key figures, what they want, and how we can swing them away from the Isolationist faction"
"Eike Study: Ingratiate herself with (one of the integrationist houses), finding out why they support further relations with the Empire and what can be done to help with that"
Notedly less hostile. Does run the risk of a catastrophic roll making our own follow-ups with the house a bit more frosty but I can't imagine she flubs it so hard she swings the vote away. Still won't succeed without the House actively wanting her to succeed, given they can casually talk rings around her without letting her find anything if they don't want her to. But as they're integrationist, they probably do want her to succeed. Ultimately, most people like talking about themselves.
May help Eike come out of her shell a little by placing her out of her "Stay still and silent" mindset, and build on what is likely her weakest stat.
Does that sound more reasonable for a first solo task?