Tikki's sticky tempo

Someone read to me when I was seven or eight years old Arlene Mosel's Tikki Tikki Tembo, and that name, slightly modified, stuck in my head ever since. I remembered it as "Ricky Ticky Tembo no-sar rembo chari-bari boochee pip perry pembo (curious readers must seek the book itself for the true name). The silly long name was more fun to say than the better known childhood favorite, super-cali-fragil-istic-exme-ala-do-cious. Well, it was on the one hand a genuine pleasure to read this book again (the name still skips and dances off the tongue) and to see the artful and whimsical illustrations of Blair Lent. On the other hand, I found it a little disturbing to realize the completely fabricated explanation for the brevity of Chinese names (mine is, of course, no exception). Such presumption smacks of cultural chauvinism. It was also upsetting to see the disparity in mother's affection for her first and second sons, and I'll hazard that many readers today would shy away from a narrative involving a little boy drowning in a well. The cover states that the story is "retold" by Mosel, but she provides no further information about a source. Does anyone know of an indigenous predecessor?

Arlene Mosel (author) and Blair Lent (illustrator)
Tikki Tikki Tembo
Henry Holt, 1968