She's pretty screwed with any path she takes since I doubt that world is egalitarian and making him attached to her (even as a toy) is going to make it impossible to escape any manhunt. The man can literally , figuratively, and actually assemble armies to hunt her down. Actually running away is wishful thinking.
Her best bet within the system that I could think of offhand is actually working with those backstabbing step-uncles/aunts. Let them know some of what she knows as a vague prophecy that she is in the process of altering, explain exactly why they were a bunch of twittering nitwits doing useless machinations for something neither she nor the emperor wanted (just for personal venting reasons. She deserves it), and use them to make it possible for her to arrange a marriage in some country far away after she thoroughly vetts the character of her suitor so that she isn't sent to another sociopath thanks to their stupidity. Maybe inject some lie about the emperor killing them for their deceit just to get them on their toes and actually commit to doing a decent job at matchmaking?
I know it almost never happens in these stories, but I would love it if one day after she's accidentally made sure he cares about her, the jig was up and she confesses to everything just to drive it home that the only person he cares about in this world thinks he's an absolute monster and she's right. He's ready to kill people at the drop of a hat. I mean, there's always a miniscule chance he was joking and the MC is an unreliable narrator, but I wouldn't blame her for taking everything he says 100% seriously.
The only other option is taking advantage of her apparent magic powers and hoping that having an adult/modern mind with the accompanied knowledge makes sorcery much easier to master.