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The takeaway seems to be, for me, a matter of keeping my right hand in what feels like an almost "underneath" position ((In reality it's where it should be - neither strong nor weak.)), with my right elbow pointed back at my hip, and keeping that right elbow close to my body throughout the swing. If I thrust my hips forward, the timing takes care of itself.

Not too far underneath. It's almost more about keeping my right elbow close to me, which pulls the hands in a bit more quickly than I've tended to do in the past.