The alternating-group wreath-product strategy conjecture

Let $A_n$ be the alternating group on $n$ letters, let $C_3$ be the cyclic group of order $3$, and let $A_n\wr C_3$ denote their wreath product. Alternating-group wreath-product strategy conjecture. There exists a surjective strategy for $A_n\wr C_3$. The claim concerns three switches generated by elements of order $3$ on the corners of a triangular table and is left as a conjectural extension of the involution case.