We use field-cycling-assisted dynamic nuclear polarization and continuous radio-frequency (RF) driving over a broad spectral range to demonstrate magnetic-field-dependent activation of nuclear spin transport from strongly hyperfine-coupled C13 sites in diamond. We interpret our observations with the help of a theoretical framework where nuclear spin interactions are mediated by electron spins. In particular, we build on the results from a four-spin toy model to show how otherwise localized nuclear spins must thermalize as they are brought in contact with a larger ancilla spin network. Further, by probing the system response to a variable driving field amplitude, we witness stark changes in the RF-absorption spectrum, which we interpret as partly due to contributions from heterogeneous multispin sets, whose zero-quantum transitions become RF active thanks to the hybrid electron-nuclear nature of the system. These findings could prove relevant in applications to dynamic nuclear polarization, spin-based quantum information processing, and nanoscale sensing.