If I were forced to hazard a guess, it would be the leak is not coming from the valleys shown but from below that (which is where we cannot see due to lack of photos). Some leaks are very, very difficult to diagnose when you’re there on the roof. That makes them near impossible to figure out with a few photos.
Find a slate or tile expert in the area and ask them to take a look. Unless it is obvious, I suspect they’re going to quote to take up a bunch of the slate in order to diagnose the problem. And that likely won’t be cheap. Or the owner can keep paying someone who doesn’t know what they’re doing a little bit at a time and unless they’re very fortunate, the leak will never be fixed.