The critical one-half conjecture for bounded-aspect-ratio ellipse packings

Let $M\geq1$, and let $\mathcal{S}$ be a packing of closed elliptical disks whose aspect ratios are at most $M$. Let $s_0\in\mathcal{S}$. Ellipse-packing critical and exponential-decay conjecture. There exists a function $f:(0,1/2)\times[1,\infty)\to(0,\infty)$ such that

$$\mathbb{P}(E_{\mathcal{S},1/2}(s_0,\infty))=0.$$

If additionally $D:=\sup_{s\in\mathcal{S}}\operatorname{diam}(s)<\infty$, then for every $0<p<1/2$ and $r>0$,

$$\mathbb{P}(E_{\mathcal{S},p}(s_0,r))\leq\exp\left(-f(p,M)\frac{r}{D}\right).$$

This extends the proposed circle-packing statements to planar ellipse packings, with the decay rate allowed to depend on the aspect-ratio bound. The source does not state a resolution.