After the previous round of experiments, I assumed that the source of my problems was the water itself. Several folks left comments suggesting that only distilled water will yield clear ice, and tap water or filtered water was simply too impure. So, I grabbed a bottle of distilled Arrowhead water and tried freezing it. Fail. Then I tried boiling twice it and freezing it. Fail.
Then, I came up with another idea… a radical idea.