I had a MEL-PVG-DTW where MEL-PVG got cancelled and I was rebooked on a flight 11 hours earlier. Called in and had no problem switching to SYD-LAX-DTW, which worked better for us anyway (original routing was purely due to award availability).

But, I was PM at the time which I'm guessing helped, and I had a logical reason why I wouldn't be able to get to MEL earlier to catch the new flight (we actually had to cancel our MEL plans as a result of all this).

A bit different circumstances, but data point that DL is willing and able to change people to a different day in the event of a schedule change. As others have said, it doesn't hurt to call and ask for the specific flights you want. Worst case they say no and you're just where you started.