Conjecture on the triangle bound for odd-wheel Cartesian powers

Let $W_t$ be the join of the cycle $C_t$ with $K_1$, let $\alpha(G)$ be the independence number, let $\chi_f(G)$ be the fractional chromatic number, and let $\Box$ denote the Cartesian product. Odd-wheel triangle-bound conjecture. For all $t\geq 3$ and all $\ell\geq 1$,

$$\frac{\alpha(W_{2t+1}^{\Box \ell}\Box K_3)}{3(2t+2)^\ell}<\frac{1}{\chi_f(W_{2t+1}^{\Box \ell})}.$$

This formalizes the authors' expectation that the triangle-based estimate is better for sufficiently large odd wheels; it is motivated by computations and remains open.