Reticketing ensures everything is smooth DoD. However, since it's a change to a different flight on same carrier, on same route, they may just revalidate the current ticket. This far put, I'd have them reticket. Call back and tell agent new ticket hasn't been issued. Don't go into all the stuff about what each agent has said. Also if you don't like new flight time, now is when to ask for a re-routed. Once reticketed you'll no longer be eligible for a free reroute, though they may still give it.