The monotonicity conjecture for percolation time in finite projective planes

Let $\Pi_q$ be a finite projective plane of order $q$, let $T_r(\Pi_q)$ denote the maximum percolation time among percolating sets at infection rate $r$, and let $r_1$ and $r_2$ be infection rates. Percolation-time monotonicity conjecture. If

$$r_1<r_2,$$

then

$$T_{r_1}(\Pi_q)\leq T_{r_2}(\Pi_q).$$

The conjecture proposes that the slowest possible percolation does not become faster as the infection rate increases. The source motivates it with exhaustive searches and random experiments, but explicitly says that the belief is not justified; no resolution is supplied.