Hi!
I actually have considered the case you are telling me and that's why I think I am doing something wrong, my intuition tells me that if h is too small, the body is indeed likely to overturn. Also to be honest I asked my professor and the answer was "You are doing something wrong" but that...
My attempt:
When the body is about to overturn backwards, the normal force and frictional force are applied on point A.
If I want to avoid overturning, torque must be 0. Then, I calculate torque with respect to A.
The value I get for h is negative, implying there is no minimum value for h...