The representation-polynomial divisibility conjecture for epimorphisms of 2-bridge knot groups

Let $\rho_1:G(K(r_1))\to SL(2,\mathbb C)$ and $\rho_2:G(K(r_2))\to SL(2,\mathbb C)$ be canonical parabolic representations, with representation polynomials $f_1(z)$ and $f_2(z)$, respectively.

Representation-polynomial divisibility conjecture. If $f_2(z)$ divides $f_1(z)$, then there exists an epimorphism

$$G(K(r_1))\to G(K(r_2)).$$

The conjecture proposes that divisibility of canonical representation polynomials detects an epimorphism between the corresponding 2-bridge knot groups. The source says the converse to the known implication appears quite likely, but supplies no proof or resolution.