It sounds like this approach could be prevented by having a random fixed offset for each user, so that you have no point of reference unless you already know where that specific user is. [Removed bit about regenerating this offset infrequently.]

EDIT: You could even do this in conjunction with the quantization mitigation, which sounds like it would shore up the slight weaknesses with that approach (where being on a quantization boundary makes it obvious where you are in that dimension) for the best of both worlds, as long as you're okay with further decreasing accuracy.