There are a few keys to doing this drill properly.  

First, keep your upper body facing down the falline.   When you do that you create a torque in your pelvis, because your feet are facing across the slope while your upper body is facing down the slope.   When it's time to execute your 180, that torque can be used as a lever to pivot your skis downhill.  Once you get them pivoting, a rotational momentum will exist that you can use to keep the pivot going until you skis are pointing across the slope in the opposite direction.  

Even with that torque to use to twist your skis, it will never work if something else doesn't happen first.  Before you can twist them, you must roll both skis downhill until they're almost flat on the snow.  When you feel them release, and begin to float, execute the 180.   No up move is needed.  Flattening your skis is all the release needed to allow the torque driven twist to happen.

Two more little tricks will help bring success with this drill.  First, keep your weight moving downhill.  This creates an fore state of balance that helps the skis to automatically seek the falline.  It's the principle that is taught in the Falline Finders drill in the Building Blocks Basic Edging DVD.  

Second, use a pole plant as you roll your skis downhill.  That pole plant acts as a secondary torque generator by which to power your 180.

The secret to not catching an edge is to not quite roll all the way to flat as you release your edges to begin your 180.  Your downhill edges should remain a whisker off the snow.  As the 180 takes place, move to flat when your skis reach the falline, then keep your downhill edges again just off the snow as you finish the turn.