Individual fractional covering conjecture for looms

Let $A$ and $B$ be hypergraphs forming an $(r,s)$-loom, and write $\mathbb{L}=(A,B)$. Let $\tau^*(A)$ and $\tau^*(B)$ denote their fractional covering numbers.

Loom component conjecture. Then

$$\tau^*(A)=s,\qquad \tau^*(B)=r.$$

The source states that this would imply the preceding loom conjecture in the equal-uniformity case and would force $|V(A)|=|V(B)|=rs$. It remains open.