I've been struggling with insomnia. Is there anything in the Satcharita about Udi helping with sleep problems?

Yes, Chapter 33 of the Shri Sai Satcharita contains specific anecdotes about Udi's effectiveness in curing sleep problems. In a footnote by R. Hari Sitaram Dixit, he recounts two instances. In one case, a friend of his had been unable to sleep for eight days despite taking a doctor's medicine. After being given Baba's Udi, he took it and slept very well throughout that night. In another similar story mentioned in Chapter 33, a friend's child who had not been able to sleep for two months was taken for Baba's Darshan in Shirdi. That very night, the child got sleep, and the problem was resolved from then on.