A convective vertical mixing scheme rooted in the Eddy-Diffusivity Mass-Flux (EDMF) approach is carefully derived from first principles in Part I. In addition, consistent energy budgets between resolved and subgrid scales when using an EDMF scheme are presented for seawater and dry atmosphere. In this second part, we focus on oceanic convection with the following objectives in mind: (\textit{i}) justify in the oceanic context the assumptions made in Part I for the derivation of an MF scheme and a new TKE turbulent transport term (\textit{ii}) show how continuous energy budgets can guide an energetically-consistent discretization (\textit{iii}) quantify energy biases of inconsistent formulations, including double-counting errors due to inconsistent boundary conditions. The performance of the proposed energetically consistent EDMF scheme is evaluated against Large Eddy Simulations (LES) and observational data of oceanic convection. We systematically evaluate the sensitivity of numerical solutions to different aspects of the new formulation we propose. Notably, when compared to LES data, energetic consistency is key to obtaining accurate TKE and turbulent transport of TKE profiles. To further illustrate that the MF concept is a credible alternative to the traditional approaches used in the oceanic context (using an enhanced vertical diffusion or a counter gradient term) the proposed scheme is validated in a single-column configuration against observational data of oceanic convection from the LION buoy.