Distinctness conjecture for the tori $\Theta^n_s$

Let $s,s_i\in(1/2,1)$, let $k_i$ be positive even integers for $i=1,\dots,l$, and assume $n=\sum_i k_i$. Consider the Lagrangian tori $\Theta^n_s$ and $\Theta^{k_1}_{s_1}\times\cdots\times\Theta^{k_l}_{s_l}$ in $(\mathbb{C}P^1)^n$. Distinctness conjecture. The torus $\Theta^n_s$ is not symplectomorphic to $\Theta^{k_1}_{s_1}\times\cdots\times\Theta^{k_l}_{s_l}$ unless $l=1$ and $s_1=s$. The conjecture is motivated by comparing counts of minimal-area Maslov-index-2 holomorphic disks and is intended to establish that these tori are distinct up to symplectomorphism, although the supplied text does not state whether it has been proved.