I believe she is reincarnated.
I believe your interpretation that Ryo, Lan Di, and Shenhua being in an eternal loop of existence, always fighting seems to fit within the series. Given that they are all virtual - maybe even literal - forms of Chinese Gods and representations of Chinese cosmology - Shenhua, phoenix; Ryo, tiger; Lan Di, dragon - it is more than possible that you are on the money here.
I suggest reading Chinese cosmology, astrology, myths, and some Taoism. All of them, especially the nature of the Yin and Yang - which is central to Taijitu and Taoism at large - is a large element of the series.
Some basic reading material:
https://en.wikipedia.org/wiki/Four_Symbols_%28China%29
"The Four Symbols (Chinese: 四象; pinyin: Sì Xiàng) are four mythological creatures in the Chinese constellations. They are the Azure Dragon (Chinese: 青龙; pinyin: Qīng Lóng), of the East, the Vermilion Bird (Chinese: 朱雀; pinyin: Zhū Què) of the South, the White Tiger (Chinese: 白虎; pinyin: Baí Hǔ) of the West, and the Black Turtle (Chinese: 玄乌; pinyin: Xuán Wū) of the North. Each one of them represents a direction and a season, and each has its own individual characteristics and origins. Symbolically and as part of spiritual and religious belief, they have been culturally important in China, Korea, Vietnam, and Japan, and also appear in many modern adaptations such as manga, and anime."
https://en.wikipedia.org/wiki/Yin_and_yang
https://en.wikipedia.org/wiki/Taoism
https://en.wikipedia.org/wiki/Chinese_astrology
In Chinese astrology, pay attention to things like the Big Dipper.