WARNING: I looked at the bits and pieces again, and it seems I might just have been lucky with the newer style baby's head. It seems to have snapped too, rather than come loose. But it snapped at the right place: right before the wider part from the protruding bit. If you look carefully at the second picture, you can still see some pink residue inside the hole of the orange body.
So if you do try anything, you should realize that there are no garantuees
It's working pretty small but the best way may just be to cleanly behead the baby using a small saw blade and the drill small holes and use a pin to re-attach the head on the new body.
I might just try something like that to save my little blond guy. Thanks for the suggestion!
And just more and more brutal ways to behead babies get added to the pile. 
I wish I could say 'no babies were harmed during ...', but, well:
