I agree with weetbix456 - most people are there Dec to March. Parks reckons about 1500 per year (across all months) do the walk.
From memory, many of the campsites are quite large, so there's always a place to hide if you need. Or you could just push on to another campsite.
Really, it's just luck of the draw. If you're flying in, you'll get an idea of how many people will be around because they'll probably be on the plane with you! (Though some might walk in from Scott's Peak, or be walking the other way, or have come in via another route).
You could do the South West Cape circuit (very basic map here
http://anpsa.org.au/APOL23/cape-ran.gif), which will be far less frequented and much more isolated.
It loops out to SW, heads north and finally loops back to Melaleuca where you fly out again.
http://mickbeckers.com/hiking/trip-repo ... -cape-tas/A nice walk, I've heard.