High-order methods guarantee high-accuracy and enhanced geometric flexibility while also entailing increased computational complexity and robustness issues. These, particularly, largely stem from aliasing errors arising in non-linear flux evaluations. Such aspect is strictly related to the difficulty of a straightforward enforcement of physical constraints on specific scalar quantities, as prescribed by conservation laws, at discrete level. What we aim to show is the extension of a computationally efficient strategy~\cite{alberti2024entropy} to enforce consistency on numerical entropy, built on top of an explicit modal DG framework, to another scalar quantity of interest, namely the kinetic energy. The numerical framework so devised is composed of a compound, explicit residual correction for entropy and kinetic energy. We show that upon selecting the interface numerical scheme of Ranocha~\cite{ranocha2020entropy}, guaranteeing both entropy conservation (EC) and kinetic energy preservation (KEP), then the obtained solution follows a physically compatible trajectory for the aforementioned scalar quantities. The structure-preserving properties are verified considering the two-dimensional Isentropic Vortex Convection case. On top of this, we draw comparison with another modal scheme capable of enforcing structure-preserving properties~\cite{chan2022entropy}, showing similar robustness properties on challenging test cases such as the Kelvin-Helmholtz and the Richtmyer-Meshkov instabilities. We further employ the designed KEP scheme to perform implicit Large Eddy simulations considering the near-incompressible Taylor-Green vortex together with the low-Mach number channel flows at friction Reynolds numbers $Re_\tau=\{180\;,590\}$. These final tests enable to show the reduction effect of the KEP modification on the scheme numerical dissipation in presence of significantly coarse space discretizations. Finally, we present the performances of the GPU-ported version of the production-grade solver, reporting both the derived speed-up, $\approx \times 10$, together with the parallel scaling on the LEONARDO HPC facility~\cite{turisini2024leonardo}.