Why are you so angry about a difference of half an hour?

Either way, DL is correct. The schedule change is small enough that it does not entitle you to a free change. Usually 90 minutes is required, or a change that makes one of your connections impossible. This is in the contract of carriage and is pretty reasonable really.

Watch for further schedule changes, one might occur that will allow you a free change. But be aware that DL can't force inventory open on other airlines so even if you end up eligible for a free change there might not be an alternative you like better.

Have an extra drink in New Orleans, it seems like you need it.