You're even righter than I thought. This is definitively faster than the method in the article. And with your method there's no point in rearranging the items. You're no more likely to have to deal with a confusing small item than with the method in the article.

The only possibly worse aspect is that, when the item is chosen, you have to make sure to identify everyone who got a copy of that item. With the method in the article you always consider items one at a time, in isolation.