The maximum-running-time comparison conjecture for infection rules

Let $H$ be an infection rule, let $M_H(n)$ be the maximum running time over all starting graphs on $n$ vertices, and let

$$M'_H(n):=\max\{\tau_H(G): G\text{ is an $n$-vertex $H$-percolating graph}\}.$$

Maximum-running-time comparison conjecture. For all infection rules $H$,

$$M_H(n)=\Theta(M'_H(n)).$$

The theorem preceding this conjecture gives a comparison for $(2,1)$-inseparable infection rules up to a constant-factor change in the number of vertices, but the general comparison remains open.