The little Schröder polynomial analogue of the q-Catalan identity

Let $R_{n,k}(q,t)$ be the $(q,t)$-Schröder polynomial obtained by weighting little Schröder paths with the statistics defined above, and let $[m]_q$ and $[m]!_q$ denote the $q$-integer and $q$-factorial. For $0\leq k\leq n-1$, little Schröder identity.

$$q^{{n\choose 2}-{k\choose 2}}R_{n,k}(q,q^{-1})=\frac{[2n-k]!_{q}}{[n]_q[n+1]_q[n-k-1]!_{q}[n-k]!_{q}[k]!_q}.$$

This conjecture is the proposed analogue for little Schröder numbers of the corresponding identity for the $(q,t)$-large Schröder polynomials; it gives a closed $q$-factorial expression for the specialization $t=q^{-1}$. Its resolution is not specified in the supplied text.