Wrathmonk:
A hangup like you see in the video is usually the result of a mis-routed static line that goes under another of the harness straps preventing the parachute bag from being pulled off the back.
The HUPRA is similar to that parachute bag in that it contains the parachute and stays with the aircraft as the parachute is pulled from it by the falling body. The HUPRA bag is affixed to a strong point on the floor adjacent to the door. A steel(?) cable attached to the parachute in the HUPRA is then passed through the D-rings of all the static lines on the affected anchor cable, (to avoid mistakes), and the devices on either end clip together to form an link that can't be undone. As has been said, the aircraft is taken to a safe height over as safe an area as possible in a gentle turn to the side the para is and the anchor cable is cut at the forward end, (I think that's where they cut it).
The warning we were always given was that once we felt ourselves go not to look up because, invariably, the metal parts of all the static lines come raining down on your head...
My guess re: control is practically none depending on how the static line was mis-routed.