How big is the influence of basis set and functional on ZPE and thermal corrections?
This is more of a comment, apologies.

Consider this paper (Ruth L. Jacobsen, Russell D. Johnson III, Karl K. Irikura, Raghu N. Kacker: Anharmonic Vibrational Frequency Calculations Are Not Worthwhile for Small Basis Sets, J. Chem. Theory Comput., 2013, 9 (2), pp 951-954). The magnitude of the computational-level-dependent scaling factors for the frequencies reported therein should give you a sense of the magnitude (I would also think that at least some other studies of the topic are cited).