Formidable multireference character is known to exist in the quartet states of the neutral radicals iron monocyanide (FeCN) and iron monoisocyanide (FeNC), even more so than the controversial FeH radical (which is now definitively known to have a (4)Delta ground electronic state). In the initial theoretical study, it was found that the gas phase adiabatic (4)Delta <- (6)Delta transition energy plummeted with improving treatment of dynamical correlation, and final results suggested that FeCN ((4)Delta) and FeNC ((6)Delta) isomers have different ground electronic states. The (4)Delta ground state for FeCN has been since verified experimentally. In this work, an ab initio composite method employing coupled cluster theory up to full quadruple excitations (CCSDTQ) and large basis set CCSDT computations is compared to multireference configuration interaction (MRCI) energies at a level of sophistication far superior to the 2004 study [DeYonker et al. J. Chem. Phys. 2004, 120, 4726]. Despite advances in the treatment of scalar relativistic effects, improved iron basis sets, and massive increases in computer processing power over the past decade, multireference methodologies still fail to find the correct ground state for FeCN, with large basis set MRCISD+Q results providing a qualitatively poor adiabatic (4)Delta <- (6)Delta transition energy, in error by nearly 5000 cm(-1). Coupled cluster theory with post-CCSD(T) additive corrections produces the (4)Delta FeCN ground state, with the (6)Delta state only 306 cm(-1) higher in energy. The ground electronic state of FeNC is computed to be (6)Delta and is only 45 cm(-1) higher in energy than the (4)Delta FeCN state while it is 741 cm(-1) lower in energy than the FeNC (4)Delta excited state. Surprisingly, an additional CCSDT additive correction for core-valence correlation shifts the FeNC transition energy in favor of a (4)Delta ground state, with a (4)Delta <- (6)Delta T-e of 227 cm(-1).