I'm not sure if I'm correct in my thinking but if your wanting to put everything into a bag, lead, hookbait the lot the best rig would be relatively short and supple as others have said.
Personally i think a shorter hook link would work better than a longer one. When it's placed in the bag it's folded on itself and so the longer the rig the more slack until the carp provides any indication at the rod.
Also when layering the hooklink into the bag with the bait. I'd think a supple braid would work better as stiffer materials may kink when being folded into the bag and result in a rig that is presented awkwardly.
If I wanted to fish a rig with a stiff section and achieve a similar baiting result, I'd probably go with a stick mix which can be threaded on maintaining a straight line.
