Ordered Ramsey conjecture for nested matchings and monotone paths

Let $M_a^\mathrm{nest}$ be a nested matching with even parameter $a$, and let $P_b^\mathrm{mon}$ be a monotone path of order $b$. Nested-matching–monotone-path conjecture. For any even $a \ge 2$ and any $b \in \mathbb{N}$, we have

$$R_\mathrm{ord}(M_a^\mathrm{nest}, P_b^\mathrm{mon}) = 1 + (a - 1)(b - 1).$$

The formula is suggested by the reported ordered Ramsey computations. No proof of the general assertion is supplied, so it remains open.