Ok I figured it out - there is an easy way.   When the object is scaled (say, smaller), its coordinate system is scaled as well, resulting in a translation of the object.  

So, you need to "undo" this translation by figuring out how far it moved.  It moves the distance equal to its distance from the origin multiplied by the scaling factor.  

So to "undo the scaling translation" simply translate by:

shift=centroid-(centroid*scalingFactor)

or

shiftX=centroidX-(centroidX*scalingFactor)
shiftY=centroidY-(centroidY*scalingFactor)

I guess this is rather obvious but I was being lazy.  Maybe it will help someone else