I've been having trouble sleeping for a while. 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 sleeplessness. In a footnote, R. Hari Sitaram Dixit recounts two such instances. First, a friend of his came to him after being unable to sleep for eight days despite trying a doctor's medicine. Dixit gave him Baba's Udi to take for three days, and the very next day, the friend reported that he had slept soundly all night after taking the Udi. In another case, a friend's child from Bandra had not been able to sleep for two months. Upon being taken to Shirdi for Baba's Darshan, the child got sleep that very night and continued to sleep well from then on.