The evaluation of quantum scattering quantities far three-body systems is explored in conjunction with the optimal separable basis methodology, which is utilized in two different ways. First, numerical results are obtained for the zero total angular momentum case using a three-dimensional discrete variable Hamiltonian with absorbing boundary conditions and optimized preconditioning. The J not equal 0 results are then estimated using helicity-conserving and J-shifting approximations, after minimizing the coriolis coupling via another application of the optimal basis method. an "effective potential" interpretation of the helicity-conserving approximation is employed, which obviates the requirement of a K-varying associated Legendre basis for the angular coordinate. This treatment also leads to an improved version of the J-shifting method that automatically incorporates centrifugal distortion and other effects. Fixed-energy cumulative reaction probabilities and thermal rate constants are presented for the O + HCl --> OH + Cl reactive scattering system.