The ability to obtain high plasma densities with high fractional ionization using readily available, low-cost components makes the helicon a candidate plasma source for many applications, including plasma rocket propulsion, fusion component testing, and materials processing. However, operation of a helicon can be a sensitive function of the magnetic field strength and geometry as well as the driving frequency, especially when using light feedstock gases such as hydrogen or helium. In this paper, we compare results from a coupled radio frequency (RF) and transport model with experiments in the axially inhomogeneous Mini-Radio Frequency Test Facility (Mini-RFTF). Experimental observations of the radial shape of the density profile can be quantitatively reproduced by iteratively converging a high-resolution RF calculation including the RF parallel electric field with a transport model using reasonable choices for the transport parameters. The experimentally observed transition into the high density helicon mode is observed in the model, appearing as a nonlinear synergism between radial diffusion, the RF coupling to parallel electric fields that damp near the plasma edge, and propagation of helicon waves that collisionally damp near the axis of the device. Power deposition from various electric field components indicates that inductive coupling and absorption in the edge region can reduce the efficiency for high-density operation. These findings can be used to optimize helicon discharges for use in Variable Specific Impulse Magnetoplasma Rocket (VASIMR) designs, and estimates for the helicon power required to perform ion cyclotron heating experiments in the Mini-RFTF are given.