Electron-ion coincidence imaging is used to study chiral asymmetry in the angular distribution of electrons emitted from randomly-oriented enantiomers of two molecules, methyloxirane and trifluoromethyloxirane, upon ionization by circularly polarized VUV synchrotron radiation. Vibrationally-resolved photoelectron circular dichroism (PECD) measurements of the outermost orbital ionization reveal unanticipated large fluctuations in the magnitude of the forward-backward electron scattering asymmetry, including even a complete reversal of direction. Identification and assignment of the vibrational excitations is supported by Franck-Condon simulations of the photoelectron spectra. A previously proposed quasi-diatomic model for PECD is developed and extended to treat polyatomic systems. The parametric dependence of the electronic dipole matrix elements on nuclear geometry is evaluated in the adiabatic approximation, and provokes vibrational level dependent shifts in amplitude and phase, to which the chiral photoelectron angular distributions are especially sensitive. It is shown that single quantum excitation of those vibrational modes which experience only a relatively small displacement of the ion equilibrium geometry along the normal coordinate, and which are then only weakly excited in the Franck-Condon limit, can be accompanied by big shifts in scattering phase; hence the observed big fluctuations in PECD asymmetry for such modes