Regardless of which solutions are dumb and which are smart, shouldn't the first step be to talk to the cursed person about it?
Maybe she just doesn't know it's there, and being a super important noble has the resources to lift the curse if only she knew she had it. Maybe she already knows it's there and it going to have it taken care of in the next couple days, meaning all your effort would be wasted. Maybe her family already has that saint on speed dial for just such an occasion.
Sure, from a reader's standpoint and knowing this is a story, it's most likely a big conspiracy by some nobles who don't like her and they're covering it up real well so the only person who could possibly help her is mr. big-dick MC. But if we're talking about MC's intelligence the stupidest thing is not starting with "hey so did you know you have a curse that'll kill you in a week or..?" so you can ask her what she thinks the best course of action is.