The Beijing leg, at least, sounds like madness to me: after hours cooped on a plane you'll spend more hours cooped in a car heading to the Great Wall and back, all this infused with tension and worry about getting back in time for your outbound flight. (You cannot afford to miss it.)
Much better to keep your brief stopover simple and just head into central Beijing and see a couple of the sights there.
thanks for the heads up, but there are certain chinese companies who do specify layover tours including pvt car/guide and they suggested its very much doable in their experience!