Having virtually no shoot through current in the biasing does not help with distortion at all.
Becuse of that fact, one must insure they have a load on the output, otherwise they have been known to go into oscillation in circuits with feed back. Giving that fact there basically isn't any shoot through currents when sitting at zero volts, the output will actually be at a Hi-z state.
As for going below common/- rail, I think that is a common problem with many op-amps. Most that advise against that normally warn of damage to the device. Bring a diode around from the low rail helps in that reguard.
I did a battery project not too long ago where I needed +/- rails on the 324 via a 9V battery. I had one section not in use so I made a relaxation oscillator out of it, drove a transistor that switched an L on the - rail of the chip with a Z diode.
When the initial system starts it has no -volts on the low rail but it will then swing to a set point via the zener diode I put there.
So when all said and done, I get my - volts on the rail and the diode serves 2 purposes, for switching and regulation. +/- 9Vs, no virtual grd.
have a good day. Jamie