Last time I did this, I would align the camera for all my characters using the SetView keybind and then right click on corpse and click on the quest item using mouse broadcasting. This got the item for all characters at the same time. However, that last time was on a private server and although I did play vanilla from the start I don't remember if that was possible back then.
That method does work in the Classic beta, or it did for the two days I was testing during the open stress test last week.
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