Record low resistivities of 10 and 30 Ω cm and room-temperature free hole concentrations as high as 3 × 10¹⁸ cm⁻³ were achieved in bulk doping of Mg in Al_0.6Ga_0.4N films grown on AlN single crystalline wafer and sapphire. The highly conductive films exhibited a low ionization energy of 50 meV and impurity band conduction. Both high Mg concentration (>2 × 10¹⁹ cm⁻³) and low compensation were required to achieve impurity band conduction and high p-type conductivity. The formation of V_N-related compensators was actively suppressed by chemical potential control during the deposition process. This work overcomes previous limitations in p-type aluminum gallium nitride (p-AlGaN) and offers a technologically viable solution to high p-conductivity in AlGaN and AlN.