The Harmonic Balance Method (HBM) transforms the search for periodic solutions of nonlinear dynamical systems into a frequency-domain problem defined by a finite set of Fourier coefficients. Coupled with a continuation scheme, the HBM supplies the Hill matrix as a natural by-product, which enables stability assessment either by conventional sorting-based Hill techniques or by the more recent Koopman-Hill approach. When the Fourier coefficients of a periodic orbit are known exactly and decay exponentially, the Koopman-Hill method comes with an exponential error bound for the computed Floquet multipliers. Stiff or non-smooth systems, however, admit periodic solutions with sub-exponentially decaying spectra. The finite truncation of the spectrum in the HBM then leads to Gibbs overshoots. Furthermore, when nonlinearities in the system dynamics are transformed back-and-forth between time and frequency domain in each solution step (alternating frequency-time method), aliasing effects occur. The resulting Fourier coefficients collected in the Hill matrix are contaminated by the superposition of harmonics beyond the Nyquist limit. We demonstrate that a deliberate choice of AFT sampling rate, while not visibly altering the signal in time, can significantly reduce the adversarial effects of aliasing when determining Floquet multipliers. For the Meissner equation, which evolves under piecewise constant parametric excitation, sampling lengths divisible by 2 but not by 4 yield Fourier coefficients with significantly reduced aliasing effects, compared to the powers of 2 that are usually employed. Based on this observation, we propose a sampling length selection strategy for AFT procedures which can improve accuracy of the resulting Floquet multipliers by multiple orders of magnitude.