Parametric models for scaling heavy-ion driver designs are described. Scaling of target performance and driver cost is done for driver parameters including driver energy, number of beams, type of superconductor used in focusing magnets, maximum magnetic field allowed at the superconducting windings, linear quadrupole array packing fraction, ion mass, and ion charge state. The cumulative accelerator voltage and beam currents are determined from the Maschke limits on beam current for each choice of driver energy and post-acceleration pulse duration. The heavy-ion driver is optimized over the large available driver parameter space. Parametric studies and the choice of a base driver model are described in a companion paper.