Translated promotion order conjecture for the dual V poset

Let $[n]=\{1,\ldots,n\}$, let $\beta$ be the restriction function on $[2]\times[b]$ defined by

$$\beta(i,j)=b+2i-1,$$

and let $\mathcal{L}_{([2]\times[b])\times[\ell]}(R^{\beta})$ denote the corresponding labeling set. Translated dual V promotion order conjecture. Promotion on $\mathcal{L}_{([2]\times[b])\times[\ell]}(R^{\beta})$ has order dividing

$$2(b+2).$$

This is a further translation of the V-poset rowmotion conjecture and remains open.