The significant environmental footprint of shipping necessitates the improvement of hydrodynamic efficiency of marine vessels so that to reduce the fuel-related pollutant emissions. To this end, shape optimization of ship hulls to minimize their resistance has become an indispensable tool in the design process of naval architecture. However, its application to vessels that employ complex propulsion systems introduces significant computational challenges. To address this issue, we developed a machine learning-assisted optimization framework using a continuous adjoint method that employs a surrogate model based on a Conditional Variational Autoencoder (CVAE). The surrogate model reconstructs the time-averaged flow field induced by a Voith Schneider Propeller using 10 ship geometric parameters and thereby replaces the computationally demanding geometrically-resolved propeller. The output of the surrogate model is used by means of implicit forcing in a finite-volume based primal/adjoint solution algorithm. The proposed framework was previously applied to a full-scale ship-hull optimization on a single-phase flow scenario by considering the input to the surrogate model to be frozen during optimization. This resulted in shapes that achieve more than 8% reduction in resistance. In this contribution we extend the existing framework to allow for its application in realistic large-scale free-floating vessels. In particular, we seamlessly integrate into the process a two-phase primal/adjoint simulation in which the ship is free to trim and sink. Additionally, we evaluate the ship geometric parameters in each optimization iteration based on the underlying mesh morphing optimization approach. The results are compared against simplified fixed-ship single-phase simulations and geometrically-resolving propeller simulations.