Spine approximation conjecture for the boundedness locus of generalized McMullen maps

For the subfamily $r_{n,a}$, let $M_n(r_{n,a})$ denote its boundedness locus, let $\mathcal{S}_n$ be its finite-$n$ spine, let $\mathcal{S}_\infty$ be the limiting spine, and let $\mathcal{N}_\varepsilon(S)$ denote the $\varepsilon$-neighborhood of a set $S$. Spine approximation conjecture. For every $\varepsilon>0$, there exists $N\geq 3$ such that for every $n\geq N$, either $M_n(r_{n,a})\subset\mathcal{N}_\varepsilon(\mathcal{S}_n)$ and/or $M_n(r_{n,a})\subset\mathcal{N}_\varepsilon(\mathcal{S}_\infty)$. Thus the boundedness locus is contained in an $\varepsilon$-neighborhood of the spine. This is proposed as a possible strengthening of the proved annular containment result, and its validity is left for future work.