Overflow is never really an issue if you always calculate time difference. (Unless the time difference is more that 50 days.)

unsigned long previousTime = millis();
... wait for some event to happen ...
unsigned long elapsedTime =  millis() - previousTime;

Even if previousTime was before the overflow, and millis() is after the overflow (so essentially millis()<previousTime), elapsedTime will still be the correct value.

This is because the calculation itself will also overflow. Since millis()<previousTime, the result would be negative, but the type of the variable is unsigned, so it wraps around. I hope that makes sense.

Just don't ever do something like if( millis() > (previousTime+1000) )

If you still want to reset millis, you can use the following:

extern volatile unsigned long timer0_millis;
unsigned long new_value = 0;

void setup(){
  //Setup stuff
}

void loop(){
  //Do stuff
  //--------

  //Change Millis
  setMillis(new_value);
}

void setMillis(unsigned long new_millis){
  uint8_t oldSREG = SREG;
  cli();
  timer0_millis = new_millis;
  SREG = oldSREG;
}