Infinitely many moduli for every order in the infinite-range case

Let $(a,b)$ be an $(a,b)$-Fibonacci sequence, and suppose it falls under case (vi) of the finite-orders conjecture, namely the case where the range of $\omega_{(a,b)}(m)$ is conjectured to be infinite. Infinite-orders conjecture. For every natural number $n$, there exist infinitely many positive integers $m$ such that

$$\omega_{(a,b)}(m)=n.$$

This strengthens the assertion that the range is infinite by predicting infinitely many moduli for each individual order. The source gives this as a further conjecture and supplies no resolution.