Microphase separating copolymers are attractive for transport applications because one microphase can solvate and allow transport of ions or small molecule penetrants, while another provides mechanical strength or other desired properties. However, the relatively low ion conductivity through such materials remains a challenge; strategies to improve cation conduction for applications such as battery electrolytes include using larger anions or a higher dielectric strength polymer (which more strongly solvates ions). These strategies effectively decrease the strength of ion-ion interactions and thus can reduce ion agglomeration and correlated cation/anion motion. However, strong ion-polymer interactions also slow ion motion, and when the polymer more strongly solvates smaller cations versus larger anions, this can lower the transference number (fraction of the conductivity contributed by the cation). We study these competing effects using coarse-grained molecular dynamics (MD) simulations which include a 1/r4 potential to capture size-dependent ion-monomer and ion-ion solvation effects. This is the same form as the interaction between an ion and an induced dipole and allows us to capture the experimentally observed trends in lamellar domain spacing and ion conductivity versus ion concentration. The impacts of ion size and polymer dielectric strength on ion correlations, diffusion, and cation conductivity in salt-doped homopolymer and block copolymer systems, along with initial results on single ion conducting systems, will be discussed.