We measure the ellipticity dependence of high-harmonic generation (HHG) from unaligned gas-phase ensembles of the five-membered ring molecules 2,3-dihydrofuran (C4H6O), furan (C4H4O), and thiophene (C4H4S). As is normally the case, the HHG emission is suppressed for increased ellipticity since the recollision wave packet leading to HHG is steered away from the parent ion for large ellipticity. However, through comparison with computations of the first step in HHG, namely, strong-field ionization (SFI), we show that the observed differences in the ellipticity dependence for the three molecular species reflect the lateral momentum distributions of the continuum electron responsible for HHG, which in turn provides information about the particular orientation between the molecular axis and the laser field that maximizes the SFI probability. Strikingly, and contrary to the conventional wisdom in the strong-field community, we find that for furan and thiophene the most probable orientation for SFI occurs when the electric field of the laser is aligned near a nodal plane of the corresponding ionizing orbital. 2,3-dihydrofuran, on the other hand, follows the standard expectation that the most probable orientation for SFI occurs when the electric field is aligned away from any nodal plane.