It looks like there’s an interesting workaround to this: using a precomp and place the pins in their initial positions.
Then, load the footage of the new head shot in a layer below.
Then, set opacity to 20% or so, on the head shot with the pins on it, so that the new head shot appears in transparency.
Move the pins so that they fit on the new head. Of course the head shot with the pins looks distorted but nevermind.
Then, replace the head shot of the precomp with the new head shot: now the pins are placed exactly as wanted.
I’ve tested it, it works.