"the theory says each point on
the dry polar should move up and to the right by a factor
equal to the square root of the sailplane’s ballasted weight
divided by its dry weight"

This is taken from one of Dick Johnson's flight test evaluations. It will not unify glider polars, but will provide the new L/D and speed to fly in order to obtain that L/D

"In this case the ballasted test gross
weight was about 957 lbs., compared to a 707 lb. dry value,
which results in a √957/707 = 1.163 ballasting factor. The measured sink rates with ballast fall fairly close to those computed by multiplying the unballasted values by the theoretical 1.163 factor. The maximum L/D still appears to be about 40.5, but it occurs at about 63 knots. This is almost 4 knots higher airspeed than one would normally expect by multiplying the dry polar’s 51-knot best L/D airspeed by the 1.163 ballasting factor."

This is just an example, but it demonstrates that the theory does not always apply in real life.