I'm having trouble sleeping. Is there anything in the Satcharita about Udi helping with sleep problems?

Yes, Chapter 33 provides examples of Udi aiding with sleep. A friend of R. Hari Sitaram Dixit had been unable to sleep for eight days and found no relief from a doctor's medicine. After being given Maharaj's Udi, he slept very well through the night. Similarly, another friend's child from Bandra had not been able to sleep for two months. After being taken to Shirdi for Maharaj's Darshan, the child got sleep that very night and continued to sleep well from then on, demonstrating the Udi's powerful effect.