I think Inaccurate/solved is resulting because of the poor scaling n the problem. In particular ,z = 1e-28 is causing difficulty in the objective function, because it makes the first additive term in the objective function of vastly different order of magnitude than the second term. As a result, the variable l is not well determined numerically to the solver. So as is, the optimal objective value is determined fairly well, but l is not well determined at all.
If z is chosen substantially larger, then the problem becomes better behaved.
Given your use of log, I advise you to follow the advice in 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 . In particular, change the MAC constraints to
r(1) <= -rel_entr(1,1+p(1)*norm(CG(1))^2)
r(2) <= -rel_entr(1,1+p(2)*norm(CG(2))^2)
r(1)+r(2) <= -rel_entr(1,1+p(1)*norm(CG(1))^2 + p(2)*norm(CG(2))^2)
However, this does not fix the Inaccurate/solved issue. You need to change z to do that.