If you use go to object or go to field to put the focus on an object inside of the pop over, the pop over will open.
I just realized that it's simpler than that. I've been struck by how a PopOver is, like a slider, really just a special kind of tab control. It then hit me that if I can give the popover itself an object name--just like you can give tab panels object names, you should be able to open the popover by using go to object and the object name assigned to the popover.
A quickie test shows that this is indeed the case.