Assume the weak energy condition (technically the Casmir effect violates it slightly, but it may not be enough to save us) and we make a black hole. The Penrose-Hawking singularity theorems apply to this case so we have singularit(ies) (i.e. GR breaks down somewhere). We don't know what type of singularity (space-like, time-like, orbifold, jump discontinuity, etc) will be created.
Now add the assumption that the limit of pressure/density for any matter or energy is positive as density grows to infinity. This is almost guaranteed given the uncertainty principle: to confine a particle to a smaller and smaller volume will take more and more energy, and in the limit of zero-volume the pressure/density ratio is that of light.
This matter can only reach infinite density with infinite space-time curvature or a perfect implosion. An isolated ball of radius r will explode with an acceleration of ~ c^2/r, so for any finite curvature there is some r below which the ball can't compress. An implosion (i.e. cavitation bubble collapse) requires perfect symmetry to make infinite densities (I believe), so can be discounted in any real scenario. Without infinite densities there are no singularities.
It seems the only way choice for our singularity is to have a space-like one, dooming any in-falling cyborg.
Most studies of charged and rotating blackhole interiors start with the hole and perturb it, rather than creating a hole through the collapse of matter starting with a regular spacetime. But this is unrealistic: the charged hole has a repulsive singularity that is a "Dirac-delta" violation of the weak energy condition and generates the divergence. The rotating hole has closed-timelike-curves. Without either of these, I believe no inner horizon can form.
Is my fatalistic reasoning correct?
This question's answer has a discussion of the singularity theorems but no mention of why the singularities would be space-like rather than time-like, etc.