So with this compressed air system, you are recovering 60% of the energy stored. I assume the 40% is lost mostly to heat when compressing the air. Why not just lift a huge weight up through a gear train, and let the weight fall to run a generator through the same gear train when you want to tap the energy you stored. The only loss there would be friction, which has to be much less than 40%.
A magnetic levitation device in vacuum can store electrical input as a mass in motion. The linear drive motor to set the mass in motion doubles as a generator in deceleration mode. The losses to magnetic drag from induced eddy currents is minimized with application of actively-controlled attractive levitation. The engineering calculations suggest one-percent loss per week in stand-by. Energy input and extraction for large storage systems should exhibit 99% efficiency.