I was not allowed to get out of the transit area at Beijing Daxing Airport for a 16 hr stopover.

You are eligible for the 24-hour visa-free transit. However, I'm not sure why they reject you to get out of the airport. The temporary entry permit is only issued as the case may be. It is not clear if you can get one in the following itinerary.

The obtaining of temporary entry permit is always a kind of roulette. It depends solely on discretionary decision of Beijing airport authorities. Many people mix up things and have a notion that 24 hour visa free transit implies a right to exit the airport when this is not the case. You right is to travel visa free, but not to exit the airport. The exit from the airport could be simply viewed as a bonus. Also, it is true that the airport authorities in Beijing are by far the most stringent in this regard.

Thank you. You have provided us the clearer answer which sums up our experience.