Common eventual period under the selective sum

Let $O=(n_1n_2\dots n_t,p_1p_2\dots p_t)$ and $P=(m_1m_2\dots m_l,q_1q_2\dots q_l)$ be two finite octal games. Write $\mathcal{G}_s$ for the scoring-play Sprague–Grundy function, and let $+_{\ell}$ denote the disjunctive sum and $\triangledown$ the selective sum.

Selective-sum period conjecture. If $\mathcal{G}_s(n+_{\ell}m)$ eventually has period $p$, then $\mathcal{G}_s(n\triangledown m)$ also eventually has period $p$.

This is proposed as a stronger form of the preceding periodicity conjecture: changing from the disjunctive sum to the selective sum should not change the eventual period. The paper gives no proof or resolution.