Conjecture on the largest 3-colourable subgraph of odd-wheel squares

Let $W_t$ be the join of the cycle $C_t$ with $K_1$, let $\alpha(G)$ be the independence number of $G$, and let $G\Box H$ denote the Cartesian product of graphs. For $t\geq 2$, consider the square $W_{2t+1}^{\Box 2}$ and its product with $K_3$. Odd-wheel square subgraph conjecture. For all $t\geq 2$,

$$(2t+2)\alpha(W_{2t+1})-\alpha(W_{2t+1}^{\Box 2}\Box K_3)=t-1.$$

Hence, the largest $3$-colourable subgraph of $W_{2t+1}^{\Box 2}$ has order $4t^2+5t+3$. This is motivated by computational observations and is presented as a future-work conjecture; no resolution is supplied.