A dunnage-producing system includes a dunnage conversion machine for converting a stock material into a relatively less dense dunnage product, a supply of stock material, and a guide element. The conversion machine is rotatable about a substantially vertical axis. The supply of stock material includes a support for the stock material that is movable relative to the conversion machine, such as for replenishing the stock material. The guide element is rotatable with the conversion machine to maintain a consistent position relative to the conversion machine, thereby consistently positioning the support relative to the conversion machine to avoid tearing or jamming problems associated with an improperly aligned supply of sheet stock material.