As long as they remained alive, their reaching the palace realm was as sure as the sun rising and setting.
When it came to the second option, while of the three it could be considered the easiest, Li Shu didn't know any palace realm expert, and she didn't even know how she could begin hiring one.
The only feasible way she could come into contact with one was if she joined a rank 3 organization, and gained their help after becoming a member, but even then, she would need to prove herself before they stepped forward to help her or they could use her condition as a leash to keep her in tow.
Besides some part of her would have felt guilty of leaving the Shao clan even after they in not so subtle terms left her to deal with her affairs alone, creating a wide berth between them and Li Shu as they could.