I'm positive that the Soviet Union didn't exist in the 7th century (page 30). It's also not a historical name for a geographical region. And you probably should have used the Chinese names for Journey of the West characters (Sun Wukon, Zhu Bajie, Sha Wujing).
If they know exactly when the boy died, why don't they just time travel to the time of the avalanche instead of following them every day?