In this work, the impacts of spurious numerical salinity mixing ($\mathcal{M}_{num}$) on the larger-scale flow and tracer fields are characterized using idealized simulations. The idealized model is motivated by realistic simulations of the Texas-Louisiana shelf and features oscillatory near-inertial wind forcing. $\mathcal{M}_{num}$ can exceed the physical mixing from the turbulence closure ($\mathcal{M}_{phy}$) in frontal zones and within the mixed layer. This suggests simulated mixing processes in frontal zones may be driven largely by $\mathcal{M}_{num}$. Near-inertial alongshore wind stress amplitude is varied to identify a base case that maximizes the ratio of $\mathcal{M}_{num}$ to $\mathcal{M}_{phy}$. We then we test the sensitivity of the base case with three tracer advection schemes (MPDATA, U3HC4, and HSIMT) and conduct ensemble runs with perturbed bathymetry. Instability growth is evaluated with several analysis methods: volume-integrated eddy kinetic energy ($EKE$) and available potential energy ($APE$), surface and bottom isohaline variability, and alongshore-averaged salinity sections. While all schemes have similar total mixing, HSIMT simulations have over double the volume-integrated $\mathcal{M}_{num}$ and 20\% less $\mathcal{M}_{phy}$ relative to other schemes, which suppresses the release of $APE$ and reduces the $EKE$ by roughly 25\%. HSIMT instabilities are confined shoreward relative to the other schemes. This results in reduced isohaline variability and steeper isopycnals, evidence that enhanced numerical mixing suppresses instability growth.