A generalized q-supercongruence with shifted summation

Let $p$ be an odd prime, let $m,r$ be positive integers with $p\nmid m$, and let $s\leqslant p-1$ be nonnegative. Write $\langle a\rangle_p$ for the least nonnegative residue of $a$ modulo $p$. The generalized q-supercongruence. If $\langle-r/m\rangle_p\equiv s+1\pmod2$, then

$$\sum_{k=s}^{p-1}\frac{(q^m;q^m)_{2k}(q^r;q^m)_k(q^{m-r};q^m)_kq^{mk}}{(q^m;q^m)_{k-s}(q^m;q^m)_{k+s}(q^{2m};q^{2m})_k^2}\equiv0\pmod{[p]^2}.$$

This is presented as a further generalization suggested by the authors; the supplied text gives no resolution.