I believe it is important to determine the cause of the deterioration before considering rehabilitation or replacement. The deterioration looks significant.
If chlorides are suspected, what would be their source, i.e. chloride laden water or calcium chloride in the original concrete mix, deicing salts used to melt snow and ice in winter climates or other? The photographs show deterioration on the underside ... what is the condition of the top surface? If the top surface of the concrete is not deteriorated than it is a possibility that chlorides in the original concrete mix combined with moisture has led to this deterioration on the underside. Chloride profiles over various slab depths would provide indicators.
Has carbonation of the structural slab been considered? I have encountered this type of deterioration a couple of times where machinery/furnace fumes were not exhausted properly. Carbonation typically occurs over long periods of time.
I have worked on several projects using hydrodemolition equipment and it works really well under the right circumstances. I have only worked on the top surface of slabs with hydrodemolition equipment although I understand there is equipment that will do vertical and soffit surfaces. The equipment is specialized and expensive.
Given the low compressive strength results for the concrete and the possibility the concrete is contaminated with chlorides, the choice of saving the slab would likely be a short term solution, deterioration will continue or even advance at a more rapid rate in the concrete you leave. Gather as much information as possible before considering the rehabilitation, total replacement or constructing a new slab below the existing slab options. The testing mentioned above will cost very little compared to the construction costs being contemplated. Concrete mix design, waterproofing, etc.. all need to be considered.