Do you consider Waldorf (Steiner) Schools alternative? In addition to the full on Waldorf schools in Taichung and Yilan, there are Waldorf programs that rent space in public schools in Taipei. I know about this thru a friend who sends his two kids to such a program in Neihu. He told me that he and his wife had to sign a waiver from the Ministry of Education acknowledging that they were aware their kids would not be assigned homework until 9th grade (I recall he said in Taiwan, not being assigned homework is considered a form of “child abuse” at least as far as the MOEd is concerned 
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Here is a relatively recent topic that mentions the Waldorf School in Yilan. They could probably guide you on what may be available in Taipei.