My recommendation: you can schedule change to pretty much any itinerary for sale with the same cities and day. So first check if there's a better one for you, even if it's more expensive. Second, DL uses Y for reaccomodation on paid tickets, thereby rendering your fare class upgradeable. So use miles to upgrade.
The schedule change has to be at least 90 minutes to get a refund. I don't understand the $60 stuff. I've never seen a schedule change result in a refare. Or are you saying you can buy the new itinerary for $60 less than the original one?
I believe OP is stating that, at the time of booking, the direct cost $60 more than the connection. OP went for the direct flight, now cancelled, and wants $60 back because the rebooking is on a cheaper fare.