Restricted Yano conjecture for generic plane curve singularities with simple monodromy

Let $\Sigma_\mu$ be the $\mu$-constant stratum of an isolated plane curve singularity germ $f:({\mathbb C}^2,0)\to({\mathbb C},0)$. Assume that no eigenvalue $\zeta\ne1$ of the monodromy is multiple; in particular, the vertices of the resolution graph have valency at most $3$. Let $(N_i,\nu_i,\delta_i)$ be the numerical data of the resolution components, and define

$$G_f(t):=t+\sum_i(\delta_i-2)t^{\nu_i/N_i}\frac{1-t}{1-t^{1/N_i}}.$$

Restricted Yano conjecture. The $b$-exponents $\{\tilde{\beta}_1,\ldots,\tilde{\beta}_\mu\}$ of a generic element of $\Sigma_\mu$ satisfy

$$\sum_{i=1}^{\mu}t^{\tilde{\beta}_i}=G_f(t).$$

This is the proposed restriction after the preceding counterexample; the supplied text gives no resolution status. It concerns the case in which nontrivial monodromy eigenvalues are simple, equivalently in the stated context the resolution graph has valencies at most $3$.