This study employs a uniform rectangular array (URA) sub-connected hybrid beamforming (SC-HBF) architecture to provide a novel self-interference (SI) suppression scheme in a full-duplex (FD) massive multiple-input multiple-output (mMIMO) system. Our primary objective is to mitigate the strong SI through the design of RF beamforming stages for uplink and downlink transmissions that utilize the spatial degrees of freedom provided due to the use of large array structures. We propose a non-constant modulus RF beamforming (NCM-BF-SIS) scheme that incorporates the gain controllers for both transmit (Tx) and receive (Rx) RF beamforming stages and optimizes the uplink and downlink beam directions jointly with gain controller coefficients. To solve this challenging non-convex optimization problem, we propose a swarm intelligence-based algorithmic solution that finds the optimal beam perturbations while also adjusting the Tx/Rx gain controllers to alleviate SI subject to the directivity degradation constraints for the beams. The data-driven analysis based on the measured SI channel in an anechoic chamber shows that the proposed NCM-BF-SIS scheme can suppress SI by around 80 dB in FD mMIMO systems.