An unstructured, low-Mach, balanced-force, volume of fluid methodology is coupled to an implicit, six-DOF overset formulation for the simulation of wave-based renewable energy devices. We propose an overlapping unstructured mesh construct that affords a wave energy converter (WEC) geometry to move freely about a background domain. A control volume finite element (CVFEM) numerical discretization, which includes novel residual-based stabilization, is developed. Credibility of this simulation tool is established by code verification, which demonstrate design-order numerics on linear and quadratic conformal and overset meshes, and model validation. A CVFEM balanced-force method is applied to a static bubble configuration using conformal and mixed topology overset meshes, while an obstructed dam break case is used to establish the viability of the proposed numerical construct. A validation hierarchy that focuses on falling and rising spheres in quiescent flow showcases the stability of the overset and six-DOF coupling approach. Finally, a buoy validation case is presented that demonstrates the efficacy of the parallel, implicit overset approach for this challenging multiphase flow regime by including both low- and high-displacement configurations along with a large wave displacement numerical benchmark with and without mooring.