Different computational techniques for cosmological phase transition parameters can impact the gravitational wave (GW) spectra predicted in a given particle physics model. To scrutinize the importance of this effect, we perform large-scale parameter scans of the dynamical real-singlet extended Standard Model using three perturbative approximations for the effective potential; the MS¯ and on shell schemes at leading order, and three-dimensional thermal effective theory (3D EFT) at next-to-leading order. While predictions of GW amplitudes are typically unreliable in the absence of higher-order corrections, we show that the reconstructed model parameter spaces are robust up to a few percent in uncertainty. While 3D EFT is accurate from one-loop order, theoretical uncertainties of reconstructed model parameters, using four-dimensional standard techniques, remain dominant over the experimental ones even for signals merely strong enough to claim a detection by LISA.