Fifteen correlated α-decay chains starting from the odd-A superheavy nucleus 289Fl were observed following the fusion-evaporation reaction 48Ca+244Pu. The results call for at least two parallel α-decay sequences starting from at least two different states of 289Fl. This implies that close-lying levels in nuclei along these chains have quite different spin-parity assignments. Further, observed α-electron and α-photon coincidences, as well as the α-decay fine structure along the decay chains, suggest a change in the ground-state spin assignment between 285Cn and 281Ds. Our experimental results, on the excited level structure of the heaviest odd-N nuclei to date, provide a direct testing ground for theory. This is illustrated by comparison with new nuclear structure calculations based on the symmetry-conserving configuration mixing theory.