We study a production of Coulomb-assisted Σ − -nucleus bound states by nuclear (K − , π + ) reactions within a distorted-wave impulse approximation, so as to examine several types of the Σ-nucleus potentials that are consistent with the available Σ − atomic X-ray data and nuclear (π − , K + ) data. We theoretically demonstrate the inclusive (K − , π + ) spectra of the Σ − unstable bound states on 28 Si, 58 Ni, and 208 Pb targets at incident K − lab momenta p K = 400-800 MeV/c.The results show that the near-recoilless (K − , π + ) reaction on the 58 Ni target gives a clear candidate to confirm properties of the Σ-nucleus potentials having a repulsion inside the nuclear surface and an attraction outside the nucleus with a sizable absorption, whereas details of the repulsion of the potential at the nuclear center cannot be determined by the inclusive spectra. This is a promising attempt to extract properties of the Σ-nucleus potential in the nucleus at forthcoming J-PARC experiments, as a full complement to the analyses of the Σ − atomic and (π − , K + ) data.