The symmetric braid index conjecture for eight small SU knots

Let $b_s(K)$ denote the symmetric braid index of a knot $K$, and consider the SU knots

$$10_{99}, 10_{123}, 10_{140}, 11_{a164}, 11_{a316}, 11_{a326}, 11_{n42}, 11_{n172}.$$

Symmetric braid index conjecture. If $K$ is one of these eight SU knots, then

$$b_s(K)>4.$$

The claim is motivated by computational searches that found no SU 4-braids for these knots, although they are not obstructed from having symmetric braid index $4$. The source presents this as evidence rather than a proved result.