i would go with pretightening the line,
wide smooth hinge,
slowing backcut as piece started to 'breathe' (show life, shift),
line over top, with guys flexing load slowly through hinge range;
to deliver as slowly and smoothly as possible to line on hinge,
then run line to matt of brush on the ground if possible,
allowing matt to 'snub' out remaining force. Or, running a de-accelerating load smoothly, but still in air, real good timing on groundie for that. Over a roof i do all this and then drew a tight stack of brush under to act as matt
To maximize when all that is called for.
Also i guess a "bouncier", longer line, would have more dampening action too
The line over the top can also double as a steering support for easily working face (placing block, cow hitch (girth w/half hitch), cutting kerf in sides to line up with backckut (to come through faster if i need to, fighting less material), lacing 1/2 hitch runnign bowline etc.