Based on the author's experience with chanting the name of Rama, is it true that this is the only practice endorsed by Sai Baba for attaining spiritual wealth?

No, that is an incorrect generalization based on a personal anecdote. The story in Chapter 19 describes the author's personal experiment to test the words of saints about nurturing good thoughts. He privately decided to chant Rama's name, and this resolve was then miraculously affirmed when he heard a stranger singing a song about Rama. This event is presented as a beautiful example of 'Sai's gift of grace without even moving his lips,' showing how he encourages each devotee's unique, sincere efforts. However, this same chapter also points to other principles, such as the Bhagavad Gita's secret of thinking of God with 'undivided attention' and the overarching rule that 'as the practice, so the benefit.' The focus is on the sincerity of the practice and the devotee's surrender, not on one specific name or method as being the only valid path.