This is the second of a series of two papers that deepen our understanding of the transversal structure and the properties of recollimation shocks of axisymmetric, relativistic, superfast magnetosonic, overpressured jets. They extend previous work that characterized these properties in connection with the dominant type of energy (internal, kinetic, or magnetic) in the jet to models with helical magnetic fields with larger magnetic pitch angles and force-free magnetic fields. In the first paper of this series, the magnetohydrodynamical models were computed following an approach that allows studying the structure of steady, axisymmetric, relativistic (magnetized) flows using one-dimensional time-dependent simulations. In this paper, synthetic radio images of the magnetohydrodynamical models are produced based on two different models to connect the thermal particle population, modeled by the hydrodynamical code, and the nonthermal particle population (added in post-processing) that causes the synchrotron radiation. The role of the magnetic tension and the Lorentz force in modeling the observational appearance of jets, namely the cross-section emission asymmetries, spine brightening, relative intensity of the knots, and polarized emission is analyzed. A cross-section emission asymmetry caused by a differential change in the angle between the helical magnetic field and the line of sight across the jet width is observed in all models and for both synchrotron emission approximations, as expected from a purely geometrical origin, for viewing angles < 10°. Models with the highest magnetizations and/or magnetic pitch angles lead to an uneven distribution of the internal energy as a consequence of the larger relative magnetic tension and radial Lorentz force, which translates into a spine brightening in the total and linearly polarized intensity maps. Force-free models display a distinct spine brightening that originates in the radial gradient of the axial magnetic field. Highly magnetized jets with large toroidal fields tend to have weaker shocks and correspondingly weaker radio knots. Signatures of this toroidal field can be found in the linearly polarized synchrotron emission for jets with large enough magnetic pitch angles and large enough viewing angles.