Tameness conjecture for automorphisms of free Bol loops of exponent two

Let $B(X)$ be a free Bol loop of exponent two. An automorphism of $B(X)$ is tame if it belongs to the group generated by the elementary automorphisms that, for a free generating set $Y=\{y_1,y_2,\ldots,y_n\}$, a chosen index $i$, and $v\in\langle Y\setminus\{y_i\}\rangle$, replace $y_i$ by $y_i v$ or by $v y_i$ and fix every other generator. Tameness conjecture. Every automorphism of a free Bol loop of exponent two is tame. The question is motivated by the positive answer for free Steiner loops, while the corresponding assertion for free Bol loops of exponent two is posed as an open problem.