The reversal-ratio conjecture for three linear extensions

Let $WRR(3)$ denote the supremum, over posets of reversal ratio with three linear extensions, of the minimum reversal ratio among their three-element realizer subfamilies. The authors' preceding discussion concerns the posets $\mathbf{Z}_{t,k}$, with $RR(\mathbf{Z}_{t,k})$ their reversal ratio.

Reversal-ratio conjecture.

$$WRR(3)=\frac{3}{4}.$$

The conjecture is motivated by the family $\mathbf{Z}_{t,k}$: the preceding lower bound would imply $WRR(3)\geq 3/4$, while the authors suspect that this family is essentially extremal. The supplied text does not establish the matching upper bound, so the equality remains open.