Don't bother with the phone. Write a quick email (specifics only, no emotion), use the complaint form on Delta.com and wait for their reply.
I don't know for sure, but I think the phone reps are limited in what they can offer.
FWIW, I had a HKG-DTW-RDU itinerary changed to HKG-NRT-HNL-LAX-RDU because of two mechanical problems (HKG-DTW and HKG-NRT) arriving 15 hours late and I was automatically given 10,000 SkyMiles. I didn't ask for more. I was a PM at the time.
Yes, the complaint button delta.com is actually a lot more useful the phone for these type of situations. If that doesn't work, write a letter and send it snail mail. I was on a GRU-ATL flight and my headset jack wasn't working. I mentioned it to the FA as dinner was being served and before I went to sleep (not really complaining but more of a FYI, this isn't working)and two days later 15K miles showed up in my account.
There are times when it's good to just roll with the punches but then there are times where poor treatment just shouldn't laughed off.