We present results from a joint theoretical and experimental study of the low-energy Penning ionization of NH3, CH3F, and CHF3 by metastable Ne(P-3(2)) and He(S-3(1)) atoms. We combine the merged neutral beams experiment, covering a range of collision energies between 0.1-150K, with multichannel quantum defect theory calculations based on interaction potentials from symmetry-adapted perturbation theory. The three symmetric tops provide several distinct properties that make them interesting targets for cold chemistry studies. Of these three, only NH3 has a lone electron pair that leads to a strong binding with rare gas atoms. The CHF3 molecule has much smaller rotational constants than both NH3 and CH3F, and thus has a considerably higher density of rotational states already at low energies. Their presence opens inelastic collision channels that reduce the observed reactive cross section. We show that this effect dominates the total rate coefficient in heavy molecules already at relatively low collision energies but is much less prominent for lighter molecules