I have used TL071, TL072 and TL074 audio opamps for many years in audio circuits with no problems. They are a TL08x selected for low noise. I used them usually with 12V or plus and minus 6V supplies.
The LM833 dual audio opamp is also good and does not have the phase inversion problem. Its minimum supply is 10V.
I have used the MC33171, MC33172 and MC33174 opamps to replace LM358 and LM324 opamps because they have many of the same spec's (minimum supply of only 3V and the same low supply current) but have much better performance. They also do not have the phase inversion problem.
The MC34071, MC34072 and MC34074 opamps also have a minimum supply of only 3V but have "normal" supply current and wider bandwidth. They also do not have the phase inversion problem.