  In Part I of this paper we have seen that any singular compact area minimizer
in a positive scalar curvature manifold admits a conformal deformation to some
minimal factor geometry that shares many properties with the minimizer, like
the Ahlfors regularity, the validity of Poincare inequalities and the presence
of tangent cones with positive scalar curvature. In this Part II we show that
these geometries admit surgery style arguments eliminating the singular sets.
