The midpoint scheme (MPS) proposed by Bartels & Prohl in 2006 is a time-marching scheme for the numerical solution of the nonlinear parabolic Landau-Lifshitz-Gilbert equation (LLG), which describes the time evolution of ferromagnetic configurations. Besides being second-order accurate in time, in contrast to competing integrators from the literature, the MPS combines a discrete energy law together with nodewise unit-length conservation. This unique combination of desirable features comes at the price of solving a nonlinear system of equations at each time step. Moreover, any proposed linearization requires a strong CFL condition, rendering the MPS considerably more expensive than competing integrators. In this talk we consider LLG involving the non-standard Dzyaloshinskii-Moriya interaction energy contribution, which is the driving force for the enucleation and stabilization of chiral magnetic skyrmions. As skyrmion dynamics turn out to be extremely susceptible to small perturbations of the micromagnetic energy, we experimentally compare the robustness and reliability of different schemes in determining critical transition material parameters. In particular, we corroborate that for such sensitive simulations the MPS, despite its higher computational cost, is the superior choice over its artificially energy-dissipating competitors.