The colorability-extension conjecture for uniform bi-hypergraphs

Let $Bi\mathcal{H}yp(n,r,m)$ denote the class of $r$-uniform bi-hypergraphs of order $n$ and size $m$. Assume $r\ge 3$ and $n\ge (r-1)^2+1$.

Colorability-extension conjecture. For any $r,m,n\in \mathbb{N}$ with $r\ge 3$ and $n\ge (r-1)^2+1$, if all bi-hypergraphs in $Bi\mathcal{H}yp(n,r,m)$ are colorable, then all bi-hypergraphs in $Bi\mathcal{H}yp(n+1,r,m)$ are also colorable.

The source notes that an analogous extension result was proved under restrictions in the $r=4$ case, and asks whether the conclusion holds without those restrictions. The unrestricted statement is left unresolved.