Following the advice in this link might help. CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions
Also (whether with or without CVXQUAD), use of Mosek rather than SDPT3 might help. The nest chance of success will be with using both CVXQUAD and Mosek.
I have no idea what the scaling is in your problem, but bad scaling can contribute to difficulties in solving. And no matter what else you do, good scaling is a good thing to have.