Recent experiments on self-diffusion in associative networks have shown superdiffusive scaling hypothesized to originate from molecular diffusive mechanisms, which include walking and hopping of the polymer chains. Since hopping requires the release of all of the stickers on the chain, it is expected that as the sticker density is increased, the walking mode will become dominant such that eventually only Fickian scaling will be observed for polymers with sticker densities above a critical value. In this work, a set of copolymers of N,N-dimethyl-acrylamide and pendant histidine groups with sticker densities ranging from 4 to IS stickers per chain was synthesized using reversible addition-fragmentation chain-transfer (RAFT) polymerization. The self-diffusion of the polymer chains in the gels in the unentangled regime was then studied using forced Rayleigh scattering (FRS). For the range of length scales measured, superdiffusive scaling was observed across the entire range of sticker densities. This suggests that molecular hopping is an important mechanism for diffusion, even for the polymer with the highest sticker density. Further analysis shows that hopping of the high-sticker-density polymer is promoted by the presence of a significant fraction of intrachain bonds, the entropic penalty associated with binding to the network, and the distribution of sticker densities inherent to copolymers synthesized through RAFT polymerization.