Any random distribution will be leaky when it is centered around the real location and multiple samples can be taken. Quantization to a desired lack of precision is the answer, nobody will be able to tell a point that happens to be rounded to itself from one that happens to be rounded from close to a neighboring cell.
If for some reason the data needs to appear random, you have to store a fixed random offset/alternative per point so that there cannot be multiple observations.
If for some reason the data needs to appear randomized between repeated lookups, you need to store a fixed offset/alternative per point and then apply an additional random offset per lookup. Repeated lookups will only leak the (badly) hidden permanently randomized stored alternative.
If for some reason the data needs to appear random, you have to store a fixed random offset/alternative per point so that there cannot be multiple observations.
If for some reason the data needs to appear randomized between repeated lookups, you need to store a fixed offset/alternative per point and then apply an additional random offset per lookup. Repeated lookups will only leak the (badly) hidden permanently randomized stored alternative.