Glock–Joos–Kim–Kühn–Osthus conjecture on packing bounded-regular graphs

Fix an integer $r$. Bounded-regular graph packing conjecture. There exists $n_0\in\mathbb{N}$ such that, for every $n\ge n_0$, any family of $n$-vertex graphs $(G_s)_{s\in[N]}$ in which each $G_s$ is $r_s$-regular with $r_s\le r$ for all $s\in[N]$, and

$$\sum_{s\in[N]}r_s=n-1,$$

packs into $K_n$. The source attributes this conjecture to Glock, Joos, Kim, Kühn and Osthus and notes that it already appears challenging for $r=3$; no resolution is given.