  We consider families of conical K\"ahler-Einstein metrics on rank one
horosymmetric Fano manifolds, with decreasing cone angles along a codimension
one orbit. At the limit angle, which is positive, we show that the metrics,
restricted to the complement of that orbit, converge to (the pull-back of) the
K\"ahler-Einstein metric on the basis of the horosymmetric homogeneous space,
which is a projective homogeneous space. Then we show that, on the symmetric
space fibers, the rescaled metrics converge to Stenzel's Ricci flat K\"ahler
metrics.
