I haven't tried your variation, Paul. But it sounds to me that you're likely to risk damaging your shoulder if you twist your body and relax the arm while uke holds it in a firm grip...
That is why you're supposed to (in my example, at least) keep your arm as close to your body as possible, using the other hand as extra help to be on the safe side.
Just a thought. As I said, I haven't tried your variation. Maybe I visualize it wrong, and there really isn't any risk of injury? Any comments?