Question:

How can I strip the existing critical points from the hull model – and not just rename them or turn them off?

    
Answer:

You can either overwrite the critical points with a Part Maker runfile, strip them from the geometry file manually or remove them from GF using MC. I would recommend using MC Fixup, in GHS, to remove critical points from GF:

READ HULL.GF
FIXUP /NOCRIT