Door open sensor?

On that car the door ajar message comes from the switches inside each door latch. The switch signals the body control module which sends the message to the dash. The long time it takes for the message when hot could be from the switch being stiff or from something else on the data buss blocking it. I would get a scan tool and use it to look at the live data and see if the switch is reporting faster than the dash is or if it's sticking. What you might try until you can scan the system would be to spray some lubricant into the door latch and then use a screwdriver to trip it and release it a few times or open and close it a few times and see if things change.