It turns out that someone else thought of that at least a couple of years ago. The Polar Ice Tray is basically a high-design cooler that separates the cloudy part of the ice from the clear part.
They accomplish this with an interior perforated bucket of sorts. The last part to freeze, the bottom, will have all the cloudy parts in it, and that is below the bucket.
According to the instructions, you break off the cloudy part outside the bucket after it is frozen.
Pretty cool. More information is here.
It looks like it works as well as my Igloo cooler method, and is just a bit smaller holding about 2.5 cups worth of ice. I've got more experiments to do though...