Instead of “Absolute Worldposition” try placing the BoundingBoxBased_0-1_UVW material function. What that does is return local space normalized to be within the object bounds. It should allow you to move the object and have the noise remain fixed relative to the object.
To match the tiling you will probably have to multiply the result by whatever your object size is. Your could even use one of the provided objectscale nodes or just use a scalar parameter and specify the scale.