Modified Xiao conjecture for the relative irregularity

Let $f\colon S\to B$ be a fibred surface, meaning a fibration from a smooth projective surface $S$ to a smooth projective curve $B$, with general fibre of genus $g\geq 2$. Write $q_f$ for the relative irregularity and call $f$ non-isotrivial when its smooth fibres are not all mutually isomorphic. Modified Xiao conjecture. For every non-isotrivial fibred surface $f\colon S\to B$ of genus $g\geq 2$, one has

$$q_f\leq \left\lceil \frac{g+1}{2} \right\rceil.$$

This modifies Xiao's original bound, which was disproved by Pirola and by later examples of Albano and Pirola. The supplied status evidence records that the modified inequality is also contradicted by those counterexamples, although they satisfy equality for the modified bound.