And I don't know if you'd need to add anything about the Coop Track being where your supply of warriors go. It felt intuitive to me and could simply be clarified in the Law of Root rather than the faction board.
An alternative solution could simply be calling it the Coop Supply or Coop Supply Track. So something like:
'Remove warriors from the supply column by column from left to right, top to bottom. If warriors return to the supply, place them on the track from right to left, bottom to top.'