We complement our earlier position-space exploration of a recently proposed S-matrix for transplanckian scattering by a momentum-space analysis. As in the previous paper, we restrict ourselves to the case of axisymmetric collisions of extended sources. Comparison between the two formulations allows for several cross-checks while showing their complementary advantages. In particular, the momentum-space formulation leads to an easier computation of the emitted-graviton spectra and to an attempt to study the system beyond its critical points into the presumed gravitational-collapse regime.