There are drywall screws that are longer (actually for double drywall). Maybe they will reach? Do screws hold well in clay otherwise?
You can also buy a few tubes of construction adhesive and apply thick lines. Clamp the board tightly and screw. If the clay is stable, then the board should be as well.
Being meticulous, I would probably run around with a longer level and mark up dips and spackle beforehand. But many also say that I am too meticulous and you wanted a Quick fix
