The requirements: Stop the disaster; raise the barrier; love the emperor
The permissive: Marriage.
The first three are mission objectives, the fourth is a side-quest. And "love" can be any flavor, unless a specific word in Korean was applied that narrows the definition. Ergo, she can love the emperor as a friend and comrade-in-arms and the conditions will be filled.
The only reason people aren't thinking about this rationally is because the emperor's temper-tantrums won't give them the space to, which is kind of brilliant on his part.