This paper makes two applications of Heisenberg's S matrix program (HSMP) to the differential cross section (DCS) of the benchmark reaction F + H-2(v(i) = 0, j(i) = 0, m(i) = 0) -> FH(v(f) = 3, j(f) = 3, m(f) = 0) + H, at a relative translational energy of 0.119 eV (total energy, 0.3872 eV), where v, j, m are vibrational, rotational, and helicity quantum numbers, respectively, for the initial and final states. (1) The first application employs a "weak" version of HSMP in which no potential energy surface (PES) is employed. It uses four simple S matrix parametrizations, two of which are piecewise continuous, and two are piecewise discontinuous, developed earlier by X. Shan and J. N. L. Connor (J. Phys. Chem. A 2012, 116, 11414-11426) for the state-to-state H + D-2 reaction. We find that the small-angle DCS is reproduced for only theta(R) less than or similar to 10 degrees when compared with the DCS for a numerical S matrix obtained in a large-scale quantum scattering computation using a PES. Here theta(R) is the reactive scattering angle. (2) In our second application, we ask the question "Can simple modifications to the parametrized S matrix be made in order to extend the agreement to larger angles?" To answer this question, we adopt a "hybrid" version of HSMP, as outlined by Shan and Connor (Phys. Chem. Chem. Phys. 2011, 13, 8392-8406), which indirectly uses PES information. We make simple Gaussian-type modifications to both the modulus and argument of the S matrix. We then obtain agreement between the DCSs for the modified and numerical S matrices up to theta(R) less than or similar to 70 degrees, a significant improvement compared with theta(R) less than or similar to 10 degrees for the unmodified parametrizations. We find that modifying the argument but not the modulus, or modifying the modulus but not the argument, fails to extend the agreement to larger angles. A semiclassical analysis is used to prove that the enhanced small-angle scattering for the "modified-modulus-modified-argument" parametrized S matrix is an example of a forward glory.