A universal approach to overcome resolution limitations in the ocean is to parametrize physical processes. The traditional method of parametrizing mesoscale range processes on eddy-permitting mesh resolutions, known as a viscous momentum closure, tends to over-dissipate eddy kinetic energy. To return excessively dissipated energy to the system, the viscous closure is equipped with a dynamic energy backscatter, which amplitude is based on the amount of unresolved kinetic energy (UKE). Our study suggests including the advection of UKE to consider the effects of nonlocality on the subgrid. Furthermore, we suggest incorporating a stochastic element into the subgrid energy equation to account for variability, which is not present in a fully deterministic approach. This study demonstrates increased eddy activity and highlights improved flow characteristics. In addition, we provide diagnostics of optimal scale separation between dissipation and injection operators. The implementations are tested on two intermediate complexity setups of the global ocean model FESOM2: an idealized channel setup and a double-gyre setup.