Pokrovskiy-type conjecture on covering finite complete hypergraphs by monochromatic Berge-cycles

For $s,k\in\mathbb{N}$ with $k\geq 2$, let $c=c(s,k)\in\mathbb{N}$ be a constant independent of $n$, and let $\mathcal{K}_{n}^{(k)}$ denote the complete $k$-uniform hypergraph on $n$ vertices. An $r$-edge-colouring assigns one of $r$ colours to every edge, and a $t$-tight Berge-cycle is a Berge-cycle in which each $t$ consecutive core vertices lie in a corresponding hyperedge. Pokrovskiy-type conjecture. For every $s,k\in\mathbb{N}$ with $k\geq 2$, there is some $c=c(s,k)\in\mathbb{N}$ such that, for every $n\in\mathbb{N}$, every $r=s(k-1)$-edge-colouring of $\mathcal{K}_{n}^{(k)}$ contains a collection of at most $s$ monochromatic $t$-tight Berge-cycles whose cores are disjoint and cover all but $c$ vertices. This generalises the graph case and is presented as a finite analogue of the paper's infinite covering results; the supplied text gives no resolution.