This work examines how inviscid interface-flux choices and Local Discontinuous Galerkin (LDG) viscous-flux parameters affect solution sensitivity and computational cost in high-order Discontinuous Galerkin Flux Reconstruction (DG-FR) simulations of compressible turbomachinery flows. A transonic low-pressure turbine cascade at M2is=1.22 and Re2is=1.5×105 is considered using a range of inviscid Riemann solvers, including Rusanov, HLLC-type solvers, RoeM and an Exact solver. The LDG discretization is varied through the penalty parameter τ and the directional parameter β. In addition to standard formulations, where the same inviscid flux is used on all interfaces, hybrid HF-R-X formulations are investigated, with Rusanov applied at wall boundaries and solver X applied on interior interfaces. The comparison is based on integrated aerodynamic forces, surface distributions of isentropic Mach number and skin friction, loss coefficients evaluated from inlet and outlet sampling planes, base pressure and normalized wall-clock time. The results show that, for the operating condition and resolution considered, lift and drag are only weakly sensitive to the inviscid Riemann solver, with variations remaining below approximately half a percent across the converged cases. Surface pressure and skin-friction trends are also nearly unchanged among the approximate solvers. Loss-related quantities are more sensitive to the numerical formulation and provide a clearer distinction between inviscid-flux and LDG-parameter choices. From a performance perspective, approximate inviscid solvers introduce only marginal overhead relative to the Rusanov baseline, whereas the Exact solver increases the wall-clock time more noticeably. The hybrid HF-R-E formulation reduces part of this cost penalty by avoiding Exact flux evaluations at wall boundaries. The dominant runtime sensitivity is associated with the LDG directional parameter: centered viscous paths with β=0 produce a substantial cost increase compared with biased paths with β=±0.5. Overall, the results indicate that inexpensive approximate inviscid fluxes are sufficient for integrated load prediction in this case, while loss prediction and computational efficiency are more strongly affected by the LDG viscous-flux construction and by the use of hybrid flux strategies.