Guo and Schlosser's generalized q-congruence for d-adic parameters

Let $d\geqslant 3$ and let $n$ be a positive integer with $n\equiv -1\pmod{d}$. Let $(a;q)_k=(1-a)(1-aq)\cdots(1-aq^{k-1})$ denote the $q$-shifted factorial, let $[m]=1+q+\cdots+q^{m-1}$, and let $\Phi_n(q)$ be the $n$-th cyclotomic polynomial. Guo and Schlosser's conjecture. For $M=((d-1)n-1)/d$ or $n-1$, one has

$$\sum_{k=0}^{M}[2dk+1] \frac{(q;q^d)_k^{2d}}{(q^d;q^d)_k^{2d}}q^{d(d-2)k} \equiv 0 \pmod{[n]\Phi_{n}(q)^3}.$$

This conjecture strengthens the known partial $q$-analogue of the corresponding supercongruence for the case $d=3$ and $n\equiv 2\pmod 3$.