We present converged quantum scattering results for the Cl + HCl - ClH + Cl reaction in which the three electronic states that correlate asymptotically to the ground state of Cl(P-2) + HCl(E-1(+)) are included in the dynamical calculations. The potential energy surfaces are taken from recent restricted open-shell coupled-cluster singles doubles with perturbative triples and multireference configuration interaction ab initio computations of A. J. Dobbyn, J. N. L. Connor, N. A. Besley, P. J. Knowles, and G. C. Schatz [Phys. Chem. Chem. Phys. 1999, 1, 957], as refined by T. W. J. Whiteley, A. J. Dobbyn, J. N. L. Connor, and G. C. Schatz [Phys. Chem. Chem. Phys. 2000, 2, 549]. The long-range van der Waals portions of the potential surfaces are derived from multisurface empirical potentials due to M.-L. Dubernet and J. M. Hutson [J. Phys. Chem. 1994, 98, 5844]. Spin-orbit coupling has been included using a spin-orbit parameter that is assumed to be independent of nuclear geometry, and Coriolis interactions are calculated accurately. Reactive scattering calculations have been performed for total angular momentum quantum number J = (1)/(2) using a hyperspherical-coordinate coupled-channel method in full dimensionality. The scattering calculations are used to study the influence of the spin-orbit coupling parameter lambda on the fine-structure-resolved cumulative reaction probabilities and transition-state resonance energies with lambda varying from -150% to +150% of the true Cl value. The results show the expected dominance of the P-2(3/2) state to overall reactivity for A close to the true Cl value and the dominance of the P-2(1/2) state for A close to -1 times the true Cl value. Between these two limits, the fine-structure-resolved cumulative reaction probabilities show oscillations as A varies, statistical behavior being recovered for lambda = 0. We present a two-state model that roughly matches these oscillations and which suggests that the reactivity oscillations are due to coherent mixing of the Omega(j) = (1)/(2) components of the 2Sigma and (2)Pi states that are derived from the P-2 states in the van der Waals regions of the potential surfaces. This mixing leads to inverted spin-orbit propensities (i.e., the upper spin-orbit state is more reactive than the lower one) for certain values of lambda. Our analysis of resonance energies indicates significant variation in resonance stability with the value of lambda, a general trend being that narrower resonances occur when |lambda| is smaller than about 50% of the absolute value of the true Cl value, suggesting that narrow resonances occur when there is significant coherent mixing. In addition, we find evidence for Stueckelberg interference oscillations in the total cumulative reaction probabilities due to a conical intersection between the 1 (2)A' and 2 (2)A' potential surfaces.