Putting your weight more balanced between the wheels will help with the steering. Chances are if you are to far forward it will make it skittish. Move your saddle and cockpit back and see if you notice the difference.

Thanks. Is there any concern that a shorter stem will increase twitchiness, thus cancelling out the move backward?

Like most things in life...it's a balancing act. Without measuring what your fore/aft weight distribution it's a guess. There is not that is a lot to work on in your post. One person's sketchy is another's 'won't turn in a 10 acre field' tight. Try it, if you don't like it go back.

I would try shifting back somewhat....I have the same bike, 120mm stem and saddle is probably neutral and the bike in no way feels skittish. In fact, I'm older and slower and most of my KOM's are downhill on the S2. Descends with confidence :)

Are the fits on the 2 bikes the same?

A quick look at the geometry charts for a 56 (assuming no changes since 2012) shows the Cannonade has a 3.3mm longer reach and a 13mm shorter stack. It also has an 18mm shorter head tube. Other dimensions show minor differences. Except for a 4mm lower drop and 2mm longer rake on the Cannonade. These are why I think the Cannonade feels more stable.

If the nose of your saddle is in front of the bottom bracket, my suspicion is that is the source of your skittish feeling on downhill descents. My suggestion would be to move your saddle back 1cm and try a 100 stem. Other than a more acute hip angle, my guess is that the weight ship will balance out the shorter stem and the bike will not be twitchy. 2cms and a 90 stem wouldn't be unreasonable, depending on how far forward your saddle currently is.