Covering conjecture for 0-isospectral lens orbifolds

Let $q$ be a positive integer, let $s_1,\dots,s_n,s'_1,\dots,s'_n$ be the parameters defining the lens orbifolds $L(q;s_1,\dots,s_n)$ and $L(q;s'_1,\dots,s'_n)$, and let $d$ be a divisor of $q$. Covering conjecture. If

$$L(q;s_1,\dots,s_n)\quad\text{and}\quad L(q;s'_1,\dots,s'_n)$$

are $0$-isospectral, then

$$L(q/d;s_1,\dots,s_n)\quad\text{and}\quad L(q/d;s'_1,\dots,s'_n)$$

are also $0$-isospectral. The corresponding statement for lens spaces was proved, whereas the numerical computations only suggested this extension to lens orbifolds and the source explains that the existing proof does not directly extend.