The odd-degree Jones coefficient nonvanishing conjecture modulo 8

Let $K$ be a knot and write

$$J_K(e^x)=1+\sum_{i=1}^{\infty}a_ix^i,$$

where $a_i$ is the degree-$i$ coefficient in the expansion of the Jones polynomial. For every integer $k\geq 1$, consider the integer $(2k+1)!a_{2k+1}$.

Odd-degree Jones coefficient nonvanishing conjecture. For every $k\geq 1$,

$$(2k+1)!a_{2k+1}\not\equiv 0\pmod{8}.$$

If true, this would allow the authors to extend their preceding congruence lemma for the even-degree invariants to the odd-degree case by an analogous argument. The conjecture is not resolved in the supplied text.