TDS are an issue. When I stopped buying bottled water in favor of the ZeroWater filters, I did notice my ice came out clearer (but not totally clear - still had a cloudy center).
When ice freezes from all sides, any contaminants OR gas molecules are forced to the center area last frozen, which makes it cloudy, even if the water is completely pure. What freezes first will be clear… and what freezes last will have any ions/gasses that exist concentrated in that area (making it cloudy).
Sorry… no matter what you do with your water, this is going to be the case. So you need the water to freeze as much as possible from one plane only. This will force the cloudiness to the opposite side of that plane.
