I prefer to use the twiddler without a strap. Sure, it rolls and slides and require one to grip and make adjustments. Personally, I find the constant change of hand/finger/wrist/elbow positions reduces overall tension as I experience more fatigue with the fingers confined to one position.
Now, when I pushes those 4 modifier keys, the twiddler naturally slides towards the pinky. This makes, for example, Control-Z difficult to chord. What I really like to have is an adjustable sticky delay that gives me just enough time to chord the combo, with the modifiers auto unstick after I am done.
Does that make sense?