A new hybrid numerical technique which utilizes both the DVR (Discrete Variable Representation) and FBR (Finite Basis Representation) to solve for the full 5D surface functions in the three-atom problem in hyperspherical coordinates for nonzero total angular momentum (J not equal 0) is reported. This method accurately treats the Eckart singularities in the kinetic energy operator which occur at both the north pole and equator of the 2D hypersphere in body-frame coordinates. The effects of the Eckart singularities on the surface function energies for HD2 are investigated and it is shown that an accurate treatment of these singularities is crucial in order to obtain the correct results. An improper treatment of the Eckart singularities could be a source for some of the discrepancies between recent experimental results and theory for the reaction H+D-2-->HD+D.