The series of salts β′′-(BEDT-TTF)2[(H2O)(NH4)2M(C2O4)3]·18-crown-6 show ambient-pressure superconductivity when M = Cr, Rh. Evidence indicates that the previously reported Cr and Rh salts show a bulk Berezinski–Kosterlitz–Thouless superconducting transition. The isostructural ruthenium and iridium salts are reported here. The Ir salt represents the first radical-cation salt to contain a 5d tris(oxalato)metalate anion. The Ru and Ir salts do not show superconductivity but instead undergo a broad chemically induced metal to insulator transition at 155 K for ruthenium and at 100 K for iridium. The c axes of the Ru and Ir salts are much shorter than those of the Rh and Cr salts. Thus, the more stable metallic state of the Cr and Rh salts is associated with the more strongly 2D electronic systems. The different low-temperature behavior of the Ru and Ir salts, which exhibit a smaller interlayer spacing, could originate from a structural change in the anionic layer which thus can be easily transmitted to the donor layers and generate a localized state. However, another possibility is that it originates from Berezinski–Kosterlitz–Thouless effects.