ObjectPicker during Prefab Edit

I have a Custom Inspector and I'm trying use the Object Picker to select one of the child objects inside my prefab, specifically while I am in "Prefab Editing Mode".

If I have a SerializedProperty for some sort of Object Reference, say a Transform, and I use PropertyField to draw it, the Object Picker picks from within the prefab with no problem.

BUT, if I roll my own ObjectField or ObjectPicker, no objects of any type show up under the 'self' tab.

Some secret magic is happening here and I can't figure out how to make it work. Anybody have any ideas?

Edit: I'm in 2019.4

 

Here's a pic that outlines the different cases: