Timing accuracy helps to some extent. The trick is to prevent current flow through the body diode. And the transient process depends on DS capacitance, output current and voltage so DT usually is based on worst case conditions. TI employs particular DC bus inductance to mitigate shoot through.Good class D output stages have high timing precision and almost no dead time
Analyze how and where timing errors are created. Use double trace oscilloscope to compare waveforms and see the delays.
There are ways to adjust DT automatically, not likely useful for audio... yet.
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