Data package accompanying the publication with the above title in Soft Matter [10.1039/d2sm00583b]. This package provides all the relevant information for numerically studying Active Brownian particles (APs) exhibiting enhanced rotational diffusion (ERD) in a quasi-two-dimensional suspension of colloidal rods. Activity couples AP-rod contacts to reorientation, with the variance therein leading to ERD. This ERD is captured by a a variant of the coupling used in our previous phenomenological modeling [10.1103/PhysRevLett.125.258002; and associated data package 10.24416/UU01-NXITLI]....