In broad terms:
There was one origin, Xinyi, coming from Ji Lonfeng.
Xinyi Liuhe is Xinyi learned by Ma Xueli, who was a Moslem. Ma learned from Ji Lonfeng
Dai Xinyi was the Xinyi taught to the Dai Family. The Dai clan already had a fighting style, so they incorporated Xinyi to it. They were the first to introduce the Five Fists.
Xingyiquan was created by Li Luoneng, based on what he learned from the Dai family. He introduced the Lizard and Tai Bird forms, and most of the linking forms.
As said, this is just a broad view. There are many details and observations and 'maybes' (some people say that no one knew what Ma Xueli's real teacher was; others say that Li Liuoneng and the Dai Family had a common teacher and Li didn't learn everything from the Dai's, etc). But that's too complicated for a single thread. And not that important
To me, Xinyiliuhe and Dai Xinyi look similar in external form (the sequences, the looks), but Xinyiliuhe and Xingyi look similar in mechanics. Have in mind, also, that there are many variations (for example, Li Tailiang's Xingyi has Che Xingyiquan AND Dai Xinyi).
I think that variations in Xingyi (what you call "add and/or subtract moves from living systems") depend on the point of view of the teachers. Xingyi and Xinyi are styles that can have many variations, as long as the mechanics and the internal aspects follow the rules and principles that would still classify them as XYQ or XY, the masters take what they consider that fits their style, body type, preferences, etc, and give it preference, or modify it.
That's the case, for example, of Wang Shujin's Xingyi. Since he was a big guy, the use of his weight gave him advance. That's what you see that his style is heavy, flowing, like a huge tank rolling down. On the other hand, Shang Yunxiang, being a small guy, modified what he had learned to create his style, that shows a quick, snapping force with explosiveness.