Concrete spall like this usually occurs in a humid area. Provide better ventilation, or crate just air flow may helps. I think the shotcrete is the way to go. Examing the reinforcing carefully to get an idea of rate/amount of deteriation. To my opinion, if the remaining concrete still has adequate strength, you may just need to make up the steel lost from corrosion. As Ron pointed out, structural steel framing action might work, but it adds dead weight, and after all, you will still have to clean and cover the defective concrete.
When you examine the existion reinf steel, keep an eye on suspecious cracks (both top and bottom, and slab and beams). Deep penetrating cracks might indicate shear failure, which speel trouble for the survival of this slab.