The theoretical formulation based on rigorous transmission-line networks is developed for a general mode conversion problem and lays the groundwork for a simpler yet more efficient graphical design approach for hybrid plasmonic mode converters (HPMCs). The concurrence of co- and cross-polarization conversion to and among higher-order photonic and HP modes followed by subsequent power redistributions and losses over the course of the HPMC can lead to performance degradation and largely determines the silicon core thickness. Using gradient ascent of the TM polarization fraction incorporated with modal index contours sets critical perturbation parameters for required transverse structural asymmetry. Polarization reversal estimates are shown to be practically applicable for about 60% of the total device length. The mode conversion efficiency (MCE), insertion loss (IL), and the polarization conversion efficiency of the proposed HPMC (<7 × 0.4 μm2) at λ0 = 1550 nm are 90.04%, 0.4691 dB, and 99.96%, respectively. The 85%-bandwidth of the MCE is 135 nm, while the IL stays below 0.5 dB over a 68-nm spectral range.