With currently known input physics and computer simulations in one dimension, a self-consistent treatment of core-collapse supernovae does not yet lead to successful explosions, while two-dimensional models show some promise. Thus, there are strong indications that the delayed neutrino mechanism works combined with a multidimensional convection treatment for unstable layers (possibly with the aid of rotation, magnetic fields and/or still existent uncertainties in neutrino opacities). On the other hand, there is a need to provide correct nucleosynthesis abundances for the progressing field of galactic evolution and observations of low-metallicity stars. The innermost ejecta is directly affected by the explosion mechanism, i.e., most strongly, the yields of Fe group nuclei for which an induced piston or thermal bomb treatment will not provide the correct yields because the effect of neutrino interactions is not included. We apply parameterized variations to the neutrino-scattering cross sections in order to mimic in one dimension the possible increase of neutrino luminosities caused by uncertainties in proto-neutron star convection. Alternatively, parameterized variations are applied to the neutrino absorption cross sections on nucleons in the "gain region" to mimic the increase in neutrino energy deposition enabled by convective turnover. We find that both measures lead to similar results, causing explosions and a Y_e > 0.5 in the innermost ejected layers, due to the combined effect of a short weak-interaction timescale and a negligible electron degeneracy, unveiling the proton-neutron mass difference. We include all weak interactions (electron and positron capture, β-decay, neutrino and antineutrino capture on nuclei, and neutrino and antineutrino capture on nucleons) and present first nucleosynthesis results for these innermost ejected layers to discuss how they improve predictions for Fe group nuclei. The proton-rich environment results in enhanced abundances of ⁴⁵Sc, ⁴⁹Ti, and ⁶⁴Zn as required by chemical evolution studies and observations of low-metallicity stars, as well as appreciable production of nuclei in the mass range up to A = 80.