Rather than replacing the "talking heads" syndrome with the "got to have an activity" syndrome (which imv tends to *stop* improvisers from being freely physical because they're busy doing the activity, and also tends to take their focus away from each other and onto the activity), try doing exercises which emphasise physical rather than verbal communication between the characters.
For example, in the middle of a scene that's got a bit "talky", side-coach simply "stop talking". I find this often leads to people really noticing for the first time what's going on between them in the scene and responding fully to each other rather than tossing words back and forth. Telling just one character to stop talking can be useful, as well.
In any exercise designed to reduce talking, you should strongly discourage the use of physical "substitute language" - i.e., trying to mime the words that you want to say, rather than letting the physical actions come from a non-wordy place.