The introduction of higher fidelity spectral models into a Discrete Ordinates Method (DOM) RTE solver introduces the challenge of solving the N(N+2) coupled equations in intensity over many spectral points. The inability to store intensity fields leads to a nonlinear increase in computational cost as compared to basic gray models, as the solution in an evolving field must be recalculated at each radiation time step. In this paper an approximate initialization approach is used to a reconstructed values of the intensities. This approach is particularly well suited to spectrally reordered methods, as the boundary conditions and scattering coefficients are gray. This approach leads to more tractable computational time, and is demonstrated using on two industrial scale flames.