Recent observations of anomalous microwave emission (AME) reveal spectral features that are not readily reproduced by spinning dust models. We examine how dust grain distributions and environmental parameters determine the peak frequency and spectral width of AME spectral energy distribution (SED). Using Monte Carlo sampling and global sensitivity analysis, we find that AME features are dominantly controlled by three parameters: grain size, shape, and a phase-dependent environmental parameter. We also quantify the effects of SED broadening from ensembles of these dominant parameters, finding that the level of tension with observations is strongly phase dependent: molecular cloud (MC) is fully consistent, dark cloud (DC) shows minor deviations, and H II regions exhibit significant offsets in peak frequency. The discrepancy in H II echoes the observed depletion of small dust grains, particularly polycyclic aromatic hydrocarbons, in H II regions. However, an observational H II region may still have AME originating from nearby non-H II clouds. In this case, model calculations for H II regions would be inappropriate. Reproducing MC and DC AME features requires ensemble variations in both grain size and environmental parameters are required to reproduce the observed spread in peak frequency and spectral width. We further propose moment expansion and emulation-based inference methods for future AME spectral analysis.