You need to improve the scaling so that there are no near zero elements which Mosek warned about.
Now that you have Mosek, you should replace CVXQUAD’s exponential.m replacement with the original CVX exponential.m .That way, CVQUAD’s Pade approximant won’t be used, and Mosek’s native exponential cone capability will be used instead.
Then follow the directions in Unable to solve convex problem with CVX and MOSEK - #3 by Mark_L_Stone so that you use the latest version of Mosek.
Then run CVX in a new MATLAB session. Then see what Mosek and CVX say about the solution to the problem.