I know of no new movements within Buddhism in the 13th century other than that of Zen. As Japan is not figured in the novel, I will take a moment to explain the form of the religion in the Himalayas. Much like Christians wait for the return of Christ, Buddhists in medieval Tibbet awaited the return of Maitreya. Maitreya (the name means loving kindness) is a bodhisattva who is to appear on Earth, achieve complete enlightenment, and teach the pure dharma.
In Tibet, lamas frequently ministered to they dying, with prayer, incantation and poetry, trying to help liberate them while in this transitory state.
Yeti are the abominable snowmen of the Himalayas, a man eating beast of great strength.
In a Buddhist monastery deep within the Himalayas, some claim there is a document which claims that Jesus, known by his Arabic name Isa, coming to India to study under the Vedic and Buddhist masters before returning to Israel as a mature man.