Big downside of Bodyguard option I am seeing is that it, pretty much explicitly, lists "may breach Oaths of College on order of Emperor".
Oaths most likely to be breached in this context are, most likely, "do not mess with imperial politics".
While I do not precisely expecting it to result in us Mindholing Elector-Counts until we find correct arguments to make them vote for the right candidate, it's still going to be a pretty dirty business. Legal, sure, but it'll probably make a certain kind of reputation.
So, nah, option to be Child Emperor's Electoral Black Ops arm is not really appealing.
Belegar's Loremaster-at-Large is extremely appealing, the only downside I can see is that K8P really needs a proper Dawi Loremaster for traditional Loremaster duties at this point. If Belegar splits those two roles of Loremaster-of-KaK and traditional Loremaster, it's pretty ideal.
Other great option is, naturally, Waystone Project. It's long-term, it involves talking to a bunch of new and interesting people, and it is going to be impactful if we succeed.
Last, at least for me, is Sylvania and Border Princedom. Those would be rather traditional CK-quests, but both seem to be rather fascinating in what they'd have us do, if for quite different reasons. But I still think that it's not quite ideal fit for Mathilde. Still, it's an option.