If you're right, then the Eye would almost certainly have to be a remnant of God or one of the other Arbiters. That, or something the story hasn't touched on at all so far, which would feel like a copout if it was some as of yet completely unnamed force in the world. Though that might explain H.E.R.O.'s big three being so strong, if they are the chosen of the last 3 Arbiters (Though I don't know how Bernhart would represent Soul if that's the case, as Malik would obviously be Chaos and Henri even more obviously Paradox) going up against the first of the altered.
My thoughts on Syla's reference to their differences seemed to be more so because the first 6 are additive, meaning there is no overlap, but together they become a greater whole, while the latter 6 were antagonistic, meaning they are equal opposites, but if you could somehow balance them, they could become something all encompassing. More simply, the first 6 are half circles, that create a whole circle, and the latter half are like yin and yang, coming together as an interconnected dichotomy to create the whole that is taiji. (Okay, so the taiji part might be weird, as we use yin and yang a lot over in the west, but not the concepts above them like wuji or taiji, but it can be interpreted as, "source of the world," according to Wikipedia, which would fit an Arbiter.)