The increase of the band gap in Zn1-xMgxO alloys with added Mg facilitates tunable control of the conduction band alignment and the Fermi-level position in oxide-heterostructures. However, the maximal conductivity achievable by doping decreases considerably at higher Mg compositions, which limits practical application as a wide-gap transparent conductive oxide. In this work, first-principles calculations and material synthesis and characterization are combined to show that the leading cause of the conductivity decrease is the increased formation of acceptor-like compensating intrinsic defects, such as zinc vacancies (VZn), which reduce the free electron concentration and decrease the mobility through ionized impurity scattering. Following the expectation that non-equilibrium deposition techniques should create a more random distribution of oppositely charged dopants and defects compared to the thermodynamic limit, the paring between dopant GaZn and intrinsic defects VZn is studied as a means to reduce the ionized impurity scattering. Indeed, the post-deposition annealing of Ga-doped Zn0.7Mg0.3O films grown by pulsed laser deposition increases the mobility by 50% resulting in a conductivity as high as σ = 475 S cm-1.