Conjecture on the radius of the Hurwitz graph of type $B_n$

Let $H(B_n)$ be the Hurwitz graph of the finite Coxeter group of type $B_n$, whose vertices are reduced reflection factorizations of a Coxeter element and whose edges are local right or left Hurwitz shifts. Radius conjecture. The radius of $H(B_n)$ is

$${n\choose 2}+1.$$

The paper has just posed the general problem of determining the radius and diameter of $H(W)$ for a Coxeter group $W$. The stated type-$B_n$ formula is presented as a conjectural target, and no resolution is supplied in the given text.