Is it possible to find the point of singularity using the BLUE shift?

As I understand your method would be suitable only for defining a single axis upon which the point of singularity would lie. In my opinion, although I can think of no reason to agree with me! you would then need to repeat the process from at least two other points in the universe, obviously these points should be a good distance from each other, to reduce errors, which would be difficult to achieve given the size of the universe.