Mary, your peeling method works superbly!
I'm too uncoordinated to hold two bowls tightly together while I shake them, so I used an empty jar like a Mason Jar, and screwed the lid on.
Shake, shake, SHAKE your garlic!
With a glass jar you can watch it happen. My big, single clove suddenly blinked, and looked like it cloned itself in a Start Trek replicator. The skin popped off WHOLE, so that it looked like a second clove.
Now, if I can just perfect a real clove-cloner, I'll never have to buy garlic again!