I think you're making an error---according to GR the singularities in black hole cores are in time, not locations in space, as confusing as that is, and as much

I think you're making an error---according to GR the singularities in black hole cores are in time, not locations in space, as confusing as that is, and as much as colloquial language suggests it. Every geodesic that crosses the horizon terminates at the singularity in a finite amount of time. If you fall past the horizon the singularity is in your definite future and in a finite amount of proper observer time your geodesic will end, at which point ... who knows what happens.