This work demonstrates the successful reconstruction of phase contrast images under challenging acquisition conditions in grating interferometry breast CT (GI-BCT) with an algorithm that adds a novel regularization functional to the existing iterative-based intensity reconstruction (IBIR) algorithm. The addition of a cross-channel regularizer allows to leverage the absorption channel’s convergence to promote that of the phase channel, which otherwise struggles to converge. We demonstrate convergence of phase contrast images on both simulations and real data. This work sets a step towards a clinically compatible reconstruction procedure using cross-channel regularization for the generation of standalone phase-contrast images of breasts.