What are the dimensions of that "object"? If they don't match the dimensions of the comp, you'll have problems. One easy fix is to animate your stills along a path in a NESTED comp that has the same dimensions as the object, then scaling & positioning it to match what you've done to that object in the main comp.
Scale??? For this to work the layer you are drawing the path on must be scaled to 100%. If not, the path you draw will not be the same size as the motion path created. Simple as that. Size of the layer has nothing to do with, scale has everything to do with it:
The path was drawn outside and inside of a 200 X 200 pixel solid. Motion path matches exactly because the layer is at 100% scale when I drew the path.
Position must be at the default also. Sorry I didn't mention that. Motion Paths are relative to the comp size so your layer must be at 100%scale and at it's default position. IOW position must be at the comp width/2 and the comp height/2.
In your situation I would set up white solid set to multiply or a null above you character, draw the mask on the null or white solid (multiply will make it disappear and yes you can draw a mask on a null and a mask may extend outside the layer and even outside the comp window), and then copy and paste.
Check carefully and you'll see that your motion path is offset exactly the same as the layer you used to draw the mask.