[mulligan]

To do the underlying with any kind of dirt/stone would require excavation big enough and deep enough to crawl under and pack the soil. IMHO , either pressure grouting (but still no way to raise the slab) or cut out the slab , properly compact the soil underneath, find the source of the problem ( no gutters, leaking pipe, etc) and re-pour the slab. That is the only way to guarantee permanent success.