paul I don't envy you. Tiling on a surface you are not sure about.
If I was really pushed to do it, I would not promise the client anything..I would have a good tap around remove the weak spots and fill with BAL rapid set. I have use it before to an inch in depth but only on a spot repair and it's held up. I would also drill some holes at 15'' intervals and BAL them in to strenghten the skim adhesion.
If the skim didn't hold up to drilling, I would stop the job. New substrate.
Just my view, others may disagree.