Current Source Inverter (CSI)-based topologies are recognized for their reliability, cost-effectiveness, and high-power handling, making them prevalent in high-power drive applications. Despite their strengths, they struggle with low-frequency harmonic torque oscillations caused due the quasi-square wave nature of the machine currents. These oscillations can trigger mechanical resonance and potential system damage, especially during start-up and low-speed operations. This paper proposes a Selective Harmonic Minimization-based Pulse Width Modulation (SHM-PWM) method for a 12-pulse CSI multi-phase induction machine drive. Using a VSI-assisted commutation method, the paper introduces a SHM-PWM strategy for self-commutated CSI and VSI-fed multi-phase induction machine drives without the need for complex commutation circuitry. The technique reduces the lower-order torque harmonics and provides a smooth torque profile, significantly improving the drive's performance during starting and low-speed operation. The methodology has been experimentally validated on a 75 kW multi-phase induction machine featuring two 1.6 kV MV windings and a 400 V LV winding.