Kuan-Lin-Yu's conjecture on zeta-like multizeta value families

Let $q=p^l>2$, let $1\leq p^m\leq q$, let $n>0$ and $r\geq 2$, and let $N_i\in \mathbb{N}\cup\{0\}$ for $0\leq i\leq n-1$ satisfy

$$1\leq \sum N_i\leq q-1.$$

If

$$(q-1)\left(q^n-\sum N_iq^i\right)\leq p^m(q-1)q^{n-1},$$

then the displayed multizeta value below is zeta-like. Kuan-Lin-Yu's conjecture. Suppose that $q>2$. Then

$$\zeta_A\left(q^n-\sum N_iq^i,p^m(q-1)q^{n-1},\ldots,p^m(q-1)q^{n+r-3}\right)$$

is zeta-like. In particular,

$$\zeta_A\left(1,p^m(q-1),p^mq(q-1),\ldots,p^mq^{r-2}(q-1)\right)$$

is zeta-like. In depth $r=3$, one additionally has

$$\zeta_A\left(1,q(q-1),q^3-q^2+q-1\right)=\frac{[3]-1}{[3][2][1]^{q^2-q-1}}\zeta_A(q^3).$$

These are conjectural families of zeta-like multizeta values arising from computer experiments based on the Chang-Papanikolas-Yu criterion. The source gives no resolution status for this conjecture; the surrounding discussion presents it as a further conjecture, while the earlier related conjecture is noted to be proved in depth $2$.