It is an open and important question whether neutrinos are Dirac or Majorana fermions, which can be unambiguously determined in neutrinoless double beta decay (NLDBD) processes. On the other hand, the combination of neutrino oscillation and cosmological measurements favors the normal hierarchy of neutrino mass ordering over the inverted hierarchy. In the three-neutrino framework, it becomes worrying that if the sum of neutrino masses lies in the "nightmare" region (0.06-0.08 eV) in the normal hierarchy, the predicted decay half-life of NLDBD may be beyond the sensitivity of next-generation ton-scale experiments. We study a well-motivated model --- minimal left-right symmetric model, which has also been extensively studied in the context of NLDBD in the literature. Different from the previous studies, we find that the diagram with the WL-WR exchange, which at the hadronic level induces long-range pion exchange, gives the leading contribution to NLDBD. We emphasize that with this new leading contribution being included there are always good prospects in future ton-scale NLDBD experiments even if future cosmological and neutrino oscillation experiments exclude the inverted hierarchy.