After reading the datasheet a few times, I think this might be the easiest:
During conversion, minimum one ADC clock cycle after the trigger event.
If you have a prescaler of 128, then one ADC clock cycle is 8 uS.
So this should work:
ADCSRA |= _BV (ADSC); // start this conversion
delayMicroseconds (8);
// change MUX channel now (ready for next conversion)