A state-selective multiconfigurational single-reference method that was outlined in the preceding paper of this series (H. Meissner and J. Paldus, J. Chem. Phys. 113, 2594 (2000); preceding paper), and is based on a quadratic iterative algorithm enabling the direct solution of the generalized Bloch equation, is applied to several model systems consisting of interacting hydrogen molecules, nowadays referred to as the H4, S4, and H8 models. These exactly solvable models are often used to test the efficacy of post-Hartree-Fock methods in their ability to recover both the dynamic and nondynamic correlation energies, since they enable a continuous variation of the degree of quasidegeneracy from the degenerate to nondegenerate limit by varying a single geometrical parameter, while simulating the dissociation of one or more single bonds. Various approximation schemes that were outlined in Part II, as well as their combinations, are tested and their performance evaluated. The size-extensivity deviations of those approximations that do not rely on the exponential cluster ansatz for the wave operator are also examined using larger hydrogen molecule clusters. It is shown that the so-called BQ(4) approximation performs extremely well in all cases and even outperforms the externally corrected, reduced multireference (RMR) CCSD in the quasidegenerate region of geometries.