  Every regular matroid is associated with a sandpile group, which acts simply
transitively on the set of bases in various ways. Ganguly and the second author
introduced the notion of consistency to describe classes of actions that
respect deletion-contraction in a precise sense, and proved the consistency of
rotor-routing torsors (and uniqueness thereof) for plane graphs.
  In this work, we prove that the class of actions introduced by Backman,
Baker, and the fourth author, is consistent for regular matroids. More
precisely, we prove the consistency of its generalization given by Backman,
Santos and the fourth author, and independently by the first author. This
extends the above existence assertion, as well as makes progress on the goal of
classifying all consistent actions.
