The QED Dyson-Schwinger equation for the inverse fermion propagator is examined for composite fermions. The photon couples to the constituent scalar of the fermions constituting the radial excitations of a hypercolour composite. A set of nonlinear mass-gap equations for the individual states is found. After having estimated the contribution of the intermediate states lying above the compositeness scale Lambda , this set is solved for a number of states below Lambda ranging from 10 to 14. Though the most elementary estimate is chosen, the results are seen to confirm those of part I: the mass spectra exhibit both the observed large mass ratios and the electron mass scale if the running coupling vanishes at hypercolour energies. In the case of a sharp cutoff, the precise values of the fine-structure constant and the electron-muon mass ratio can be reproduced; fourteen states below Lambda are predicted for Lambda approximately=10¹⁵ GeV. The muon-tau mass ratio comes out to be too large and, therefore, nonsharp cutoffs are studied. The complete solution of the mass equations is presented. This reveals a pronounced decrease of the muon-tau mass ratio. The effect is independent of the kind of non-sharp cutoff chosen and persists when extending the mass loop integration to larger values of q² or when varying the number of states below Lambda while keeping alpha at 1/137 and m₁/m₀ at 207. Extending the loop integration to still larger values of q², distinctive effects of 'spectral inversion' are found, in particular, the effect m_L/m tau >_tau/m_mu (m_L denotes the fourth charged lepton mass). These results suggest the existence of 11-12 charged lepton states below Lambda approximately=10¹⁵ GeV and 40 GeV<m_L<50 GeV. Sequential Dirac neutrinos should exist above M_Z/2.