Monotonicity conjecture for metered parking functions

Let $m,n$ be positive integers, and let $\mathrm{mpf}_{m,n}(t)$ denote the number of $t$-metered $(m,n)$-parking functions. Monotonicity conjecture. If $t_1<t_2$, then

$$\mathrm{mpf}_{m,n}(t_2)\leq \mathrm{mpf}_{m,n}(t_1).$$

This conjectures that the number of metered parking functions is nonincreasing as the number of meters varies, despite the lack of set containment between the corresponding sets. The supplied text gives no resolution, so the conjecture is treated as open.