Uniqueness conjecture for consistent sandpile torsor algorithms on oriented regular matroids

Let $M$ be an oriented regular matroid, equipped with triangulating circuit and cocircuit signatures. A consistent sandpile torsor algorithm is a consistent algorithm assigning sandpile torsor actions with this auxiliary data. The BBY algorithm is one such algorithm, and its structure includes the four variants obtained by independently replacing the circuit or cocircuit contribution by its negative. Uniqueness conjecture. Every consistent sandpile torsor algorithm for the class of oriented regular matroids with the auxiliary data of triangulating signatures has the same structure as the BBY algorithm. This is presented in the source as a remaining mystery, and no resolution is supplied.