Shell model calculations for the neutron-rich N=126 206Hg – 197Lu (Z=80–71) isotones were performed with two different parametrisations. The one refined to explain the isomerism in 204Pt was found to be the only one able to reproduce the more recent data on 203Ir, and in general, to give a better reproduction of the nuclei in this region. For more exotic nuclei approaching the r-process path, this refined parametrisation predicts the existence of isomeric states with spin-parities 5- and 10+ in the even-mass and 19/2+ in the odd-mass isotones. Also, it predicts ground-state spin-parities of 3/2+ for 201Re and 11/2- for 199Ta and 197Lu, with low-energy long-lived isomers present. The remaining deficiencies of the interaction are related to the properties of the d5/2 orbital and are influenced by octupole collectivity. The presented predictions provide guidance and can be tested in the near future at radioactive-beam facilities.