Snappy“things that are slung”
Slung? If you're thinking of something more violent than "set down" or "put down", you can say "throw down".
lift up - set (back) down is my preferred pair. Then there's get down - put (back) up.
Let's lift up this box and then set it down over there.
Let's get this box down from the shelf and then put it back up on this shelf over here.
CJ