Well off the top of my head there's, poison, learning how to defend yourself, running away, disguises, hiring assassins.
She spent so much time and effort trying to pretend she's mental and in the process she not only got hurt but risked her life which kind of defeats the purpose of her trying to live.
All her brothers are watching her though. As soon as they saw her trying to do any of that they’d kill her. The best way is to make them think you aren’t a threat thus they shift their attention to each other. Try any of the things you mentioned and they, who probably were already trained, would kill her before she could properly execute any of that. If it was a single sibling intent on killing her I would understand, but that wasn’t the case.
I thought of that as well, and i was going to add on that if her goal is to seem harmless and nonthreatening there's still other methods she could have used, instead of risking her life. Like instead of going crazy as in acting like a lunatic, she could have pretended to mentally revert back to a childlike state due to trauma, or act like she became really dumb and incapable of any manipulation. But because her goal was to survive and avoid her death I listed those methods, and I'm right because her pretending to be crazy did not work out in the end, as in she almost died due to her own antics and due to the prince not liking her crazy dance thing.
I think the reason why she went for the crazy route instead of the naive/dumb route is because the brothers know that if she is crazy, then she is a danger to herself. Remember when she almost died because she climbed the walls with thorns? Or when she is walking all bloodied up? These just proved that they dont need to kill her because she is basically walking to her demise.
If she chose to be dumb, they would still kill her because you know she is not crazy enough to kill herself.
That sounds like a plot hole because she wants to survive but she's putting herself in situations where she could actually die, like the thorn incident where she herself thought she was going to die for real. I also think my original statement still stands, almost killing yourself to continue the act of lunacy because you don't want to be killed, just seems impractical.

I feel as if there are better ways to survive than pretend you're crazy ヾ(❀╹◡╹)ノ~