I heard Udi can help with sleep problems. Are there any specific examples of this in the text?

Yes, Chapter 33 provides two distinct examples of Udi helping with sleep issues, both recounted in a footnote by R. Hari Sitaram Dixit. In the first case, a friend of Dixit's had been unable to sleep for eight consecutive days and found no relief from a doctor's medicine. After taking Baba's Udi as suggested, he reported the very next day that he had slept soundly through the night. The second instance involves a friend's child in Bandra who had not been able to sleep for two months. Upon being taken to Shirdi for Maharaj's Darshan, the child got sleep that very night and continued to sleep well thereafter, demonstrating the powerful effect of Baba's grace and Udi.