Burcroff's irredundance conjecture for direct products of balanced complete multipartite graphs

Let $G=\prod_{i=1}^n K[u_i,t_i]$ be a direct product of balanced complete multipartite graphs. The independence number $\alpha(G)$ is the largest size of an independent set, and $\operatorname{IR}(G)$ is the maximum size of an irredundant set. Burcroff's conjecture.

$$\alpha(G)=\operatorname{IR}(G).$$

This strengthens the earlier conjecture that the independence number equals the upper domination number for these products. The conjecture is known in the cases $t_n\leq 2$ and $n\leq 3$, but the source does not establish its general resolution.