> Our house sits on a post-tension cable concrete slab. Is it possible to cut
> through such a slab and dig a shelter below it?

No. We've got the same kind of slab, and our condo association documents provide this warning:
"Each residential structure in the Development has been constructed on a post-tension concrete slab. This slab is approximately 12 inches thick and contains stressed steel cables. Any drilling, excavating or other disturbance of the slab could damage the slab and cables and could result in serious injury. If damaged, the slab will not function as designed."

Where's the water table in Houston? How far down do you dig before you hit water?