Why invert at all?
Your audio system (except possibly the motors for turntable, tape, and player), runs on DC. You just need a DC-DC converter, which are almost noiseless. Better yet, you may find equipment that runs on your house DC.
Of course, this means surgery on your electronics to bypass that noisy power supply. But it's minor surgery, suitable for DIY.
I use battery power for my phono / pre, and am thinking about converting to batteries for amps as well. As it is, my system is black - and SMOOTH. No sharp edges here.
Batteries forever!