To clarify, the objective is not to obtain heavy water. It is to obtain light water. So it is not an issue if the ice contains only some deuterium, but mostly light water, as the point is that the liquid water now has less deuterium than it did before.
I actually just got a reply from a DDW manufacturer who said the following:
"Deuterated ("heavy") water has a higher freezing point than ordinary water, there is indeed a fractionation slightly above zero Celsius, but it does not mean that all heavy water will be frozen.
By holding the temperature at let’s say 1°C, you can get some ice that contains D2O or DHO in a higher concentration than in liquid because the freezing point for H2O is lower.
This way you can reduce the D-concentration of the water with 8-10 ppm in one step. If you wish to achieve further decrease you have to freeze this water in further steps.
According to our knowledge, fractional distillation is the best way to produce DDW in large scale."
This same manufacturer says that home water distillers can at best reduce deuterium concentration by 1 or 2 PPM per pass, which is much less efficient than commercial evaporative methods. But an 8 to 10 drop in PPM from a freezing method (per pass) is considerable (if true), as the early clinical trials in this field suggest that even drops of say 20ppm are potentially clinically significant.