Slurry grouting - the engineer actually said no-one can predict what might happen if a slurry containing water was introduced into a 4000+ year old dry environment. One of the implications being that slurry might destabilise the structure.

Pressure grouting - rejected on the grounds that it was only normally done when you'd already created a sufficiently stable and strong structure.

With either method what you could not ensure was that all the voids would be filled.