Barry / Big Bear -
Your driveway doesn't look particularly steep to me. By itself, it should not cause the problem you have experienced.
It appears that the tips of your springbars are WAY too high, and that would be a big part of the problem. As I think you observed in the narrative with the pictures, a tight turn (as shown in one pic) can cause the tip of the bar to hit stuff on the underside of the A-frame at the snap-up hook area. It can also cause the chain on the outside of the turn to snub up against the A-frame, effectively shortening it. Either one will cause immense stresses on the various parts, with the result you have experienced.
With the tow vehicle and TM hooked up on level ground, and the springbars raised to the proper tension, the bars should be level with the ground, or even pointed slightly down. If the tips are too high (as shown in your pics), you can tilt them down by tilting the ballmount backward. This will increase the distance between the tips and the snap hook, and therefore between the tips and the A-frame. Compare the first picture
here with the pictures of your rig.
It appears to me that the biggest part of the problem occurs during a tight turn - and the transition to a sloped driveway merely makes it worse. The quick answer, as others have stated, is to release the springbars before backing in. But get those tips down first!
Bill