Rohatgi's almost-every matching conjecture for ordered Ramsey numbers

Let $M^<$ be an ordered matching on $n$ vertices with interval chromatic number $hi$, and let $K^<_3$ be the ordered triangle. For a positive integer $hi$, there is a constant $psilon(hi)>0$ such that

$$R_<(M^<,K^<_3)\leq O(n^{2-psilon(\chi)})$$

for almost every ordered matching $M^<$ on $n$ vertices with interval chromatic number $hi$.

Rohatgi's conjecture. The stated subquadratic bound holds for almost every ordered matching of each fixed interval chromatic number.