If you have binary plus exponential cone (log), I think the only options in CVX are to use Mosek as solver (preferred) or CVXQUAD + Mosek or Gurobi (not preferred).
As for help with understanding Gurobi Sub-optimal termination, Root relaxation unbounded
, perhaps you can get help at https://support.gurobi.com/hc/en-us/community/topics .